The user wants a self-contained HTML file with:
1. 20 numbered balls (1-20) dropping from the center of a heptagon
2. Heptagon spins 360 degrees every 5 seconds
3. Balls affected by gravity and friction
4. Balls collide with each other
5. Balls bounce off rotating walls realistically
6. Show each ball's spin via rotation of its number
7. Implement all collision detection myself
8. No external resources/CDN/network

This is a physics simulation. I'll need to write a complete HTML file with CSS and JavaScript.

Key components:
- Canvas-based rendering
- Heptagon with 7 vertices, center screen
- Balls with numbered labels that render as rotating text
- Gravity pulling balls down
- Friction/damping
- Self-collision between balls (circle-circle)
- Wall collision with rotating heptagon (circle-polygon)

For the rotating wall collision, I need to:
1. Define heptagon vertices in local space (perfect heptagon)
2. Apply rotation transform each frame
3. For each ball, detect collision with walls (edges of heptagon)
4. Reflect velocity based on wall normal, accounting for wall rotation/movement
5. Push ball out of wall to prevent sticking

For ball-ball collision:
1. Detect if distance < sum of radii
2. Separate balls
3. Exchange momentum (elastic collision with equal mass assumption or just basic elastic)

For rendering numbers spinning:
- Each ball has angle from velocity/tangential force? Actually user says "show each ball's spin via rotation of its number". I should track rotation angle of each ball, update it based on angular velocity from collisions with walls or other balls.
- When ball hits a wall, its spin changes based on tangential velocity change
- When ball hits another ball, spin changes based on friction at contact

Let me design this carefully.

Heptagon:
- 7 sides, center at canvas center
- Radius R (big enough)
- Local vertices: (R * cos(2π*k/7), R * sin(2π*k/7)) for k=0..6
- Rotate angle θ = (2π/5) * t where t is time in seconds (since 5s per 360°)
- World vertices = rotated local vertices added to center

Ball physics:
- Position (x, y)
- Velocity (vx, vy)
- Radius r (all same, maybe 12-15px)
- Mass (proportional to area or just equal)
- Angular velocity ω
- Angle θ (for number display)
- Coefficient of restitution e.g. 0.8 for bounce
- Friction coefficient μ for tangential spin

Gravity:
- g = 800 px/s^2 or so
- Apply to vy each frame

Integration:
- Use small timestep or multiple substeps for stability
- Check collisions in each substep

For wall collision with moving polygon:
- For each edge of heptagon
- Find closest point on segment to circle center
- If distance < radius, collide
- Normal pointing into polygon
- Relative velocity: v_ball - v_wall_at_contact
- For rotating wall: v_wall_at_contact = ω_wall × (contact_point - center) perpendicular to radius
  Actually: if polygon rotates with angular velocity Ω, velocity at point P is Ω * (P - center) rotated 90° CW
- Reflect relative velocity along normal
- Apply restitution to normal component
- Friction applies to tangential component, changes ball angular velocity

Ball-ball collision:
- Standard elastic collision for equal masses (just exchange normal velocities if no friction)
- Separate overlapping balls
- Friction at contact can add spin

Let me build this step by step.

Timestep: use fixed dt = 1/120 or so for stability, but since it's JavaScript I'll use requestAnimationFrame with accumulated time and maybe 4-8 substeps per frame.

I'll make the canvas fullscreen.

Let me write the code.

```javascript
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
```

Heptagon:
```javascript
const numSides = 7;
const polyRadius = 300; // or dynamic based on screen
const polyAngularSpeed = (2 * Math.PI) / 5; // rad/s
```

Vertices:
```javascript
function getPolyVertices(time) {
    const angle = polyAngularSpeed * time;
    const cx = canvas.width / 2;
    const cy = canvas.height / 2;
    const verts = [];
    for (let i = 0; i < numSides; i++) {
        const a = angle + (2 * Math.PI * i) / numSides;
        verts.push({ x: cx + polyRadius * Math.cos(a), y: cy + polyRadius * Math.sin(a) });
    }
    return verts;
}
```

Balls:
```javascript
const balls = [];
const numBalls = 20;
const ballRadius = 14;
for (let i = 0; i < numBalls; i++) {
    balls.push({
        x: cx + (Math.random() - 0.5) * 10,
        y: cy + (Math.random() - 0.5) * 10,
        vx: (Math.random() - 0.5) * 20,
        vy: (Math.random() - 0.5) * 20,
        angle: 0,
        angVel: 0,
        number: i + 1,
        mass: 1 // or area
    });
}
```

Wait, user says "dropping from the center". So start all at center, but maybe slightly offset so they don't all perfectly overlap initially causing infinite collision force. Or I can spread them a tiny bit. Actually with 20 balls at same spot, it'll explode naturally once gravity/initial tiny random velocity acts. But to avoid huge forces, I'll start them with tiny random offsets inside a small circle.

Physics update per substep:
```javascript
function update(dt) {
    // Gravity
    const g = 1200;
    for (const b of balls) {
        b.vy += g * dt;
    }
    
    // Move
    for (const b of balls) {
        b.x += b.vx * dt;
        b.y += b.vy * dt;
    }
    
    // Wall collisions
    const verts = getPolyVertices(currentTime);
    const cx = canvas.width / 2, cy = canvas.height / 2;
    for (const b of balls) {
        // Check each edge
        for (let i = 0; i < numSides; i++) {
            const p1 = verts[i];
            const p2 = verts[(i + 1) % numSides];
            // closest point on segment
            const dx = p2.x - p1.x;
            const dy = p2.y - p1.y;
            const len2 = dx*dx + dy*dy;
            let t = ((b.x - p1.x)*dx + (b.y - p1.y)*dy) / len2;
            t = Math.max(0, Math.min(1, t));
            const closestX = p1.x + t * dx;
            const closestY = p1.y + t * dy;
            const distX = b.x - closestX;
            const distY = b.y - closestY;
            const dist = Math.sqrt(distX*distX + distY*distY);
            if (dist < ballRadius) {
                // normal (from wall to ball)
                const nx = distX / dist;
                const ny = distY / dist;
                // push out
                const overlap = ballRadius - dist;
                b.x += nx * overlap;
                b.y += ny * overlap;
                
                // wall velocity at contact point (only rotation)
                // center is (cx, cy)
                const rx = closestX - cx;
                const ry = closestY - cy;
                const wallVx = -polyAngularSpeed * ry; // perp to radius for CCW positive
                const wallVy = polyAngularSpeed * rx;
                
                const relVx = b.vx - wallVx;
                const relVy = b.vy - wallVy;
                const vDotN = relVx * nx + relVy * ny;
                if (vDotN < 0) { // moving towards wall
                    // tangential direction
                    const tx = -ny, ty = nx;
                    const vDotT = relVx * tx + relVy * ty;
                    
                    const restitution = 0.7;
                    const newNormal = -restitution * vDotN;
                    const friction = 0.3;
                    const newTang = vDotT * (1 - friction); // simplified friction
                    
                    b.vx = (newNormal * nx + newTang * tx) + wallVx;
                    b.vy = (newNormal * ny + newTang * ty) + wallVy;
                    
                    // Apply friction to spin
                    // tangential relative velocity at ball surface = vDotT
                    // change in angular velocity = friction * vDotT / r
                    // sign: if wall moving tangential relative to ball...
                    b.angVel += -friction * vDotT / ballRadius * 2; // tuning
                }
            }
        }
    }
    
    // Ball-ball collisions
    for (let i = 0; i < numBalls; i++) {
        for (let j = i + 1; j < numBalls; j++) {
            const a = balls[i], b = balls[j];
            const dx = b.x - a.x;
            const dy = b.y - a.y;
            const dist2 = dx*dx + dy*dy;
            const minDist = ballRadius * 2;
            if (dist2 < minDist * minDist && dist2 > 0.0001) {
                const dist = Math.sqrt(dist2);
                const nx = dx / dist;
                const ny = dy / dist;
                const overlap = minDist - dist;
                // Separate equally (since equal mass)
                a.x -= nx * overlap * 0.5;
                a.y -= ny * overlap * 0.5;
                b.x += nx * overlap * 0.5;
                b.y += ny * overlap * 0.5;
                
                const dvx = a.vx - b.vx;
                const dvy = a.vy - b.vy;
                const vDotN = dvx * nx + dvy * ny;
                if (vDotN > 0) {
                    const restitution = 0.9;
                    const impulse = -(1 + restitution) * vDotN / 2;
                    a.vx += impulse * nx;
                    a.vy += impulse * ny;
                    b.vx -= impulse * nx;
                    b.vy -= impulse * ny;
                    
                    // tangential friction affecting spin
                    const tx = -ny, ty = nx;
                    const vDotT = dvx * tx + dvy * ty;
                    const friction = 0.2;
                    a.angVel += -friction * vDotT / ballRadius;
                    b.angVel += friction * vDotT / ballRadius;
                }
            }
        }
    }
    
    // Update spin
    for (const b of balls) {
        b.angle += b.angVel * dt;
        // damping
        b.angVel *= 0.999;
    }
}
```

Rendering:
```javascript
function draw() {
    ctx.clearRect(0, 0, canvas.width, canvas.height);
    const verts = getPolyVertices(currentTime);
    ctx.beginPath();
    ctx.moveTo(verts[0].x, verts[0].y);
    for (let i = 1; i < numSides; i++) {
        ctx.lineTo(verts[i].x, verts[i].y);
    }
    ctx.closePath();
    ctx.strokeStyle = '#ff0';
    ctx.lineWidth = 4;
    ctx.stroke();
    
    for (const b of balls) {
        ctx.save();
        ctx.translate(b.x, b.y);
        ctx.rotate(b.angle);
        ctx.beginPath();
        ctx.arc(0, 0, ballRadius, 0, Math.PI * 2);
        ctx.fillStyle = '#fff';
        ctx.fill();
        ctx.strokeStyle = '#333';
        ctx.lineWidth = 2;
        ctx.stroke();
        ctx.fillStyle = '#000';
        ctx.font = 'bold 14px sans-serif';
        ctx.textAlign = 'center';
        ctx.textBaseline = 'middle';
        ctx.fillText(b.number, 0, 0);
        ctx.restore();
    }
}
```

Wait, the user says "spin via the rotation of its number". The number should rotate with the ball. My code above does that since I translate to ball position, rotate by b.angle, then draw circle and text.

Need to make sure collision detection is robust. With substeps it should be okay.

I should also add some air friction/damping so they don't keep bouncing forever with same energy. Or maybe slight damping (0.9999 per step).

Let me refine the code to be more polished, single file.

Also need to handle window resize.

Potential issue: 20 balls inside a heptagon, gravity down. They should settle at the bottom. The walls rotate, so balls get swept around. This should look cool.

For wall collision relative velocity: if the wall is moving, the restitution should apply in the frame of the wall. My code does that.
Friction: I used simplified friction by clamping or multiplying tangential component. Better model: impulse with friction.

Actually let's use a proper friction model for collision:
Normal impulse: Jn = -(1+e)*vRelN / (1/m1 + 1/m2)
Tangential impulse: Jt = -μ * |Jn| * sign(vRelT) or Coulomb friction
But this is getting detailed. For visual effect, simple is fine.

However, since user explicitly asks to implement collision detection myself and show realistic bounce, I'll make it decent.

Let me think about stability. If I use single timestep equal to frame time (~16ms), it might miss collisions. Better to use substeps.

```javascript
const substeps = 8;
const subDt = dt / substeps;
for (let s = 0; s < substeps; s++) {
    update(subDt);
}
```

Also when checking wall collisions, need to ensure the closest point logic works on segments.

One subtlety: if dist is 0 (ball center exactly on closest point), normalize fails. Handle by skipping or using fallback.

Also, I need to update currentTime for polygon rotation. Use elapsed time.

Let me write the final HTML. I'll make it look nice with dark background.

Canvas size: full window. For high DPI, maybe scale, but not necessary.

Polygon radius should fit screen. Let's set it to min(w,h) * 0.35 or something.

Let me double check ball count: 20.

Spin: balls should spin when they collide. I think tracking spin and showing rotating numbers is good.

I should ensure balls don't get stuck in walls. The separation push is important.

Also maybe add a slight damping coefficient for linear velocity (air resistance) so they settle.

Let me code this up carefully.

Edge case: all 20 balls starting at exactly center will all be overlapping. Initial push from overlap resolution + gravity + tiny random velocity will spread them out. But overlap resolution for 20 balls at same point might be jittery. Let me start them in a small cluster.

Actually, let's spawn them in a small circle in the center with slight random offsets and tiny velocities. That will look like they drop from the center.

```javascript
for (let i = 0; i < 20; i++) {
    const a = (2 * Math.PI * i) / 20;
    const r = 5 + Math.random() * 5;
    balls.push({
        x: cx + Math.cos(a) * r,
        y: cy + Math.sin(a) * r,
        vx: (Math.random() - 0.5) * 10,
        vy: (Math.random() - 0.5) * 10,
        ...
    });
}
```

This avoids perfect overlap.

Now for the collision detection: I need to check ball vs walls and ball vs balls. The polygon has 7 edges. The polygon rotates.

I should perhaps compute the rotation angle per frame and keep consistent.

Let's structure the code:

```html
<!DOCTYPE html>
<html>
<head>
    <style>
        body { margin: 0; overflow: hidden; background: #111; }
        canvas { display: block; }
    </style>
</head>
<body>
    <canvas id="c"></canvas>
    <script>
        // all code here
    </script>
</body>
</html>
```

Now the script:

```javascript
const canvas = document.getElementById('c');
const ctx = canvas.getContext('2d');

function resize() {
    canvas.width = window.innerWidth;
    canvas.height = window.innerHeight;
}
window.addEventListener('resize', resize);
resize();

const numSides = 7;
const rotationPeriod = 5; // seconds
const angularSpeed = (2 * Math.PI) / rotationPeriod;

const numBalls = 20;
const ballRadius = 14;
const balls = [];
const gravity = 800;
const restitution = 0.75;
const wallFriction = 0.3;
const ballFriction = 0.2;
const linearDamping = 0.9995;

function getCenter() {
    return { x: canvas.width / 2, y: canvas.height / 2 };
}

function getPolyRadius() {
    return Math.min(canvas.width, canvas.height) * 0.35;
}

function getVertices(time) {
    const center = getCenter();
    const r = getPolyRadius();
    const theta = angularSpeed * time;
    const verts = [];
    for (let i = 0; i < numSides; i++) {
        const a = theta + (2 * Math.PI * i) / numSides;
        verts.push({ x: center.x + r * Math.cos(a), y: center.y + r * Math.sin(a) });
    }
    return verts;
}

const cx0 = canvas.width / 2;
const cy0 = canvas.height / 2;
for (let i = 0; i < numBalls; i++) {
    const a = (2 * Math.PI * i) / numBalls + (Math.random() - 0.5) * 0.2;
    const r = ballRadius + Math.random() * 20;
    balls.push({
        x: cx0 + Math.cos(a) * r,
        y: cy0 + Math.sin(a) * r,
        vx: (Math.random() - 0.5) * 40,
        vy: (Math.random() - 0.5) * 40,
        angle: 0,
        angVel: (Math.random() - 0.5) * 4,
        number: i + 1,
        mass: 1
    });
}

function update(dt, time) {
    // Apply gravity
    for (const b of balls) {
        b.vy += gravity * dt;
    }
    
    // Update position
    for (const b of balls) {
        b.x += b.vx * dt;
        b.y += b.vy * dt;
        b.vx *= linearDamping;
        b.vy *= linearDamping;
    }
    
    const verts = getVertices(time);
    const center = getCenter();
    
    // Wall collisions
    for (const b of balls) {
        for (let i = 0; i < numSides; i++) {
            const p1 = verts[i];
            const p2 = verts[(i + 1) % numSides];
            const ex = p2.x - p1.x;
            const ey = p2.y - p1.y;
            const len2 = ex * ex + ey * ey;
            if (len2 === 0) continue;
            let t = ((b.x - p1.x) * ex + (b.y - p1.y) * ey) / len2;
            t = Math.max(0, Math.min(1, t));
            const closestX = p1.x + t * ex;
            const closestY = p1.y + t * ey;
            const rx = b.x - closestX;
            const ry = b.y - closestY;
            const dist = Math.sqrt(rx * rx + ry * ry);
            if (dist < ballRadius && dist > 1e-6) {
                const nx = rx / dist;
                const ny = ry / dist;
                // push out
                const overlap = ballRadius - dist;
                b.x += nx * overlap;
                b.y += ny * overlap;
                
                // velocity of wall at contact point due to rotation
                const cpx = closestX - center.x;
                const cpy = closestY - center.y;
                const wallVx = -angularSpeed * cpy;
                const wallVy = angularSpeed * cpx;
                
                const relVx = b.vx - wallVx;
                const relVy = b.vy - wallVy;
                const vDotN = relVx * nx + relVy * ny;
                
                if (vDotN < 0) {
                    const tx = -ny;
                    const ty = nx;
                    const vDotT = relVx * tx + relVy * ty;
                    
                    const newRelVx = -restitution * vDotN * nx + (vDotT * (1 - wallFriction)) * tx;
                    const newRelVy = -restitution * vDotN * ny + (vDotT * (1 - wallFriction)) * ty;
                    
                    b.vx = newRelVx + wallVx;
                    b.vy = newRelVy + wallVy;
                    
                    // tangential relative motion at contact changes spin
                    // friction force direction relative to ball surface:
                    // if relative velocity is +t, friction opposes, causing negative torque
                    const spinImpulse = -wallFriction * vDotT / ballRadius;
                    b.angVel += spinImpulse * 3;
                }
            }
        }
    }
    
    // Ball-ball collisions
    for (let i = 0; i < numBalls; i++) {
        for (let j = i + 1; j < numBalls; j++) {
            const a = balls[i];
            const c = balls[j];
            const dx = c.x - a.x;
            const dy = c.y - a.y;
            const dist2 = dx * dx + dy * dy;
            const minDist = ballRadius * 2;
            if (dist2 < minDist * minDist && dist2 > 1e-6) {
                const dist = Math.sqrt(dist2);
                const nx = dx / dist;
                const ny = dy / dist;
                const overlap = minDist - dist;
                // position correction
                const corr = overlap * 0.5;
                a.x -= nx * corr;
                a.y -= ny * corr;
                c.x += nx * corr;
                c.y += ny * corr;
                
                const dvx = a.vx - c.vx;
                const dvy = a.vy - c.vy;
                const vDotN = dvx * nx + dvy * ny;
                if (vDotN > 0) {
                    const impulse = -(1 + restitution) * vDotN * 0.5;
                    a.vx += impulse * nx;
                    a.vy += impulse * ny;
                    c.vx -= impulse * nx;
                    c.vy -= impulse * ny;
                    
                    const tx = -ny, ty = nx;
                    const vDotT = dvx * tx + dvy * ty;
                    a.angVel -= ballFriction * vDotT / ballRadius;
                    c.angVel += ballFriction * vDotT / ballRadius;
                }
            }
        }
    }
    
    // Update rotation
    for (const b of balls) {
        b.angle += b.angVel * dt;
        b.angVel *= Math.pow(0.2, dt); // spin friction/damping
    }
}

function draw(time) {
    ctx.clearRect(0, 0, canvas.width, canvas.height);
    
    const verts = getVertices(time);
    ctx.beginPath();
    ctx.moveTo(verts[0].x, verts[0].y);
    for (let i = 1; i < numSides; i++) {
        ctx.lineTo(verts[i].x, verts[i].y);
    }
    ctx.closePath();
    ctx.strokeStyle = '#0ff';
    ctx.lineWidth = 4;
    ctx.lineJoin = 'round';
    ctx.shadowColor = '#0ff';
    ctx.shadowBlur = 10;
    ctx.stroke();
    ctx.shadowBlur = 0;
    
    for (const b of balls) {
        ctx.save();
        ctx.translate(b.x, b.y);
        ctx.rotate(b.angle);
        
        // ball body
        ctx.beginPath();
        ctx.arc(0, 0, ballRadius, 0, Math.PI * 2);
        ctx.fillStyle = '#fff';
        ctx.fill();
        ctx.strokeStyle = '#222';
        ctx.lineWidth = 2;
        ctx.stroke();
        
        // number
        ctx.fillStyle = '#000';
        ctx.font = `bold ${ballRadius}px sans-serif`;
        ctx.textAlign = 'center';
        ctx.textBaseline = 'middle';
        ctx.fillText(b.number, 0, 0);
        
        ctx.restore();
    }
}

let lastTime = performance.now();
let time = 0;

function loop(now) {
    let frame = (now - lastTime) / 1000;
    if (frame > 0.05) frame = 0.05; // cap
    lastTime = now;
    time += frame;
    
    const substeps = 8;
    const subDt = frame / substeps;
    for (let s = 0; s < substeps; s++) {
        update(subDt, time);
    }
    
    draw(time);
    requestAnimationFrame(loop);
}

requestAnimationFrame(loop);
```

Wait, there might be an issue with reading `c` as variable name; let me rename inner loop ball to `ball2` or `other`.

Also, the spin damping exponent: `Math.pow(0.2, dt)` seems odd. I'd prefer `Math.exp(-spinDamping * dt)`. Let's use `0.5` per second? `Math.exp(-3 * dt)`.

Let me refine and make it robust.

Another issue: the polygon center might move if balls push against it? No, it's a kinematic body, fixed center.

Also, when computing closest point on segment, if the segment is very short (degenerate), skip.

Let me also add some visual flair: maybe a subtle grid or gradient? No, keep it simple.

Also, `canvas.width/height` set inside resize. The initial center should use canvas size after resize.

One more thing: after window resize, the polygon radius changes. The balls might be outside the new smaller polygon. It's okay, they'll be pushed back in quickly.

Let me check the physics logic for wall collision again.

The relative velocity: `relV = v_ball - v_wall`.
Contact normal `n` points from wall toward ball (out of polygon? Actually my segments are indexed CCW or CW?).

If vertices are generated with:
```javascript
const a = theta + (2 * Math.PI * i) / numSides;
```
As i increases, angle increases, so it's counter-clockwise. For CCW polygon, interior is left of each edge. The vector from p1 to p2 is along the edge. The outward normal (pointing into interior? Wait). For CCW, the outward normal is to the right of the edge? Let's think.

Edge from p1 to p2. Cross product of edge with normal should be positive for inward normal? Actually, if polygon is CCW, the normal pointing inward (toward interior) is to the left of the direction vector. Left-hand normal: (-ey, ex). Right-hand normal: (ey, -ex).

So for a CCW polygon, `p2.x - p1.x, p2.y - p1.y`. Inward normal = `(-(p2.y - p1.y), (p2.x - p1.x))` normalized. Outward normal = `((p2.y - p1.y), -(p2.x - p1.x))`.

The interior is where the center of the heptagon is. Since center is average of vertices (or explicitly set), it should be inside. The vector from closest point on edge to ball center (`rx, ry`). If ball is inside polygon, this vector points away from wall toward interior? Actually if ball is inside, closest point is on wall, vector from wall to ball points inward. If ball is outside (but we only have inside balls because gravity and bounds), it points outward. But our balls should be inside the heptagon most of the time (unless they tunnel out due to fast rotation at corners). Actually, the heptagon spins, balls might end up outside if thrown. The simulation should still work, but normal direction should be consistent.

In my code, if ball is inside and collides, `dist = |ball - closest|`. Since ball is inside, `ball - closest` points inward. My `nx,ny` points inward. I push ball along `nx,ny` to separate it from wall (i.e., push into polygon). That is correct: if inside and touching wall, push inward.

For reflection: if ball is inside and moving toward wall, `vDotN < 0` means it's moving in direction of `-nx` (outward), so away from wall? Wait. `n` is inward. If ball moves outward (toward wall, which is inward direction? No, wall is at boundary. Inward direction is into polygon. Outward direction is away from center.

If `vDotN < 0`, it means velocity dot `nx` (inward) is negative, so ball is moving outward. Since `nx` points inward, moving outward means moving toward the wall. So we should bounce when `vDotN < 0`. Yes.

Then reflected relative velocity normal component: `newVn = -e * vDotN` (positive means now moving inward). Good.

Then `newV = newVn * n + (1-friction)*vDotT * t` where `t` is tangent.

Then `b.vx = newVx + wallVx`. But I computed:
`b.vx = -restitution * vDotN * nx + (vDotT * (1-wallFriction)) * tx + wallVx`
Wait, that seems to miss something: `newRelV` should be in the frame of the wall. So `b.vx = newRelVx + wallVx`. And `newRelV = newRelVn * n + newRelVt * t`. With `newRelVn = -restitution * vDotN` and `newRelVt = vDotT * (1 - friction)`. So:
`b.vx = -restitution * vDotN * nx + vDotT*(1-wallFriction)*tx + wallVx`.
That's what I have. Good.

For spin: change in angular velocity proportional to tangential relative velocity. I used:
`b.angVel += spinImpulse`.
`spinImpulse = -wallFriction * vDotT / ballRadius`.
Radius? I scaled by 3 for effect, but maybe I should use 1/ballRadius to be correct. Let me think physically.
Tangential friction force magnitude = μ * normal force. Impulse ≈ μ * Jn / ballRadius? No, for a rigid collision, the change in linear velocity tangent is limited by friction. The resulting angular velocity change: J_tangential / (m * r) * direction? Actually, if a tangential impulse `Jt` acts at the contact point, it changes spin by `Jt / (m r^2)` for point mass? Wait, I = m r^2 / 2 for solid disk or 2/5 m r^2 for sphere. But since mass cancels out if we think just about kinematics, `angVel += Jt / (I/m * r)`. Anyway, for visual effect, just `vDotT / r` is fine. I'll use `b.angVel += -wallFriction * vDotT / ballRadius` (no extra scaling).

Similarly for ball-ball.

I think the code is ready. Let me polish the HTML.

I should probably use a nicer font, but sans-serif is fine.

Add some instructions or just start.

Also, make sure the canvas is focused for keyboard? No need, no keyboard.

Maybe add a slight transparency to the polygon or balls? Keep solid.

One more thing: the user says "Show 20 numbered balls (1 to 20) dropping from the center". So they should start near center and fall. My initial placement with small radius and random offsets works.

Wait, I need to be careful about the ball's angular velocity update. Since I redraw in the same coordinate frame after rotation, the number should rotate correctly.

Let me write the final file content.

Let me double check variable names in the code snippets to avoid typos.

Actually, I want to make the polygon a bit larger and the ball size proportional to screen? ballRadius = 14 is fine but maybe 16. Let's use 15.

Also, maybe use `ctx.fillStyle = '#000'` for numbers, but on white balls that's fine.

I'll add a subtle drop shadow to balls for depth.

Also, the heptagon could be drawn with a fill or just outline. Let's use semi-transparent fill:
```javascript
ctx.fillStyle = 'rgba(0, 255, 255, 0.1)';
ctx.fill();
```
And then stroke.

Actually, maybe a nice dark background and neon walls.

```css
body { margin: 0; overflow: hidden; background: #0a0a0a; }
```

Wall color: cyan `#00ffff`.
Ball fill: white or slightly off-white.

Let me also make sure the script handles the first frame well with `lastTime` initialization.

And I should handle `performance.now()` correctly. Yes.

Now, the integration scheme. With Euler and substeps, it should be stable enough. 8 substeps per frame is good.

Push out from walls: if overlap is large due to tunneling, multiple substeps should resolve it gradually.

One more check: the `vDotT` in wall friction. `1 - wallFriction` means friction reduces tangential component proportionally. But friction should be a coefficient that determines how much tangential impulse is applied. For small dt, this is fine.

For ball-ball, same idea.

Also, I added `linearDamping` to velocity slightly each step (0.9995 per 1/120s step). At 120 steps per second, damping per second = `0.9995^120 ≈ 0.94`. That's a 6% loss per second. Might be okay. Let's make it less aggressive: `0.9998` per step gives ~0.78 per second. Or maybe `0.9999` (0.88 per second). Let's just use `0.9999` per step or no linear damping and just rely on restitution < 1 for energy loss. Yes, restitution < 1 already dissipates energy. I don't need linear damping. Let me remove that.

Spin damping: keep it, otherwise spin never dies.

Final code structure looks solid. Let me write it out.

Actually, I realize I used `c` for ball2 in nested loop but `c` is also the canvas id. Not a problem because different scopes, but let me rename to `other` to avoid confusion.

Also, I need to adapt to window resize properly. When resize happens, the polygon center changes, but balls stay where they are. That's fine.

One last thing: in the vertex generation, using `canvas.width/2` every frame is okay but slightly wasteful. But fine.

Let me write the file.

The file has been written successfully. Let me verify it exists and check if it looks correct by reading it back.

The file has been written successfully and contains all the requested features:
- 20 numbered balls (1-20) dropping from the center
- Spinning heptagon (360° every 5 seconds)
- Gravity applied
- Ball-ball collisions implemented from scratch
- Wall collisions with rotating polygon implemented from scratch
- Spin visualized via rotation of the number on each ball
- Single self-contained HTML file with inline CSS and JS
- No external resources/CDN/network requests

The physics simulation includes:
- Circle-circle collision detection and response (elastic with equal mass impulse + friction for spin)
- Circle-segment collision detection for the rotating heptagon walls
- Moving wall support (computes wall velocity at contact point due to rotation)
- Positional correction to prevent sinking
- Friction at contacts that affects angular velocity (spin)
- Spin damping so balls eventually stop spinning
- Sub-stepping for stability

I should confirm completion to the user.