The task: write a single-page web app in index.html. We have three.min.js present in current directory. Need to load via <script src="three.min.js"></script>. Build interactive 3D Rubik's Cube with clickable face rotations, orbit-drag camera, and a scramble button. No external resources.

We need to write index.html with necessary style and script.

We need to examine three.min.js? Not needed maybe but confirm file exists. Let's list directory.

Only three.min.js present. We need to create index.html.

Implement: Use Three.js to create cube made of 27 smaller cubes (without center). We'll color stickers as per faces. Simpler: each small cube is a box with colored faces. Implement raycasting for click detection; when clicking a cube face, determine which layer to rotate based on face normal and direction (mouse drag? But requirement: clickable face rotations – clicking a face triggers rotation of that face by 90 degrees. Provide scramble button that performs random rotations.

Orbit controls: Since we cannot use external libs, we need to implement simple orbit controls manually with mouse dragging: rotate camera around center.

Alternatively we can embed OrbitControls from three.min.js if present? No; three.min.js includes core only. We could embed minimal orbit controls code within script.

Implement simple orbit: maintain spherical coordinates theta, phi, radius; adjust on mouse move; update camera position.

For rotating cube layers: we can group the relevant cubies into a temporary THREE.Group, animate rotation (90 deg) then commit.

Time constraints: we need to produce code that works.

Let's design: Create scene, camera (PerspectiveCamera), renderer.

Create an array of cubies: for x,y,z in -1,0,1 positions. Each cubie is a Mesh with BoxGeometry(0.9,0.9,0.9). Material can be an array of 6 MeshBasicMaterial with colors for stickers: For each face direction, assign a color if that face is outer (i.e., if coordinate equals +1 or -1). Provide black for internal faces. Provide stickers using small planes? Simpler: color whole face; internal faces black; That will show colored squares on outer faces.

Assign colors: Up (+y) white, Down (-y) yellow, Front (+z) red, Back (-z) orange, Right (+x) blue, Left (-x) green.

Create raycaster on click. On click, intersect objects. Get intersected cubie and face index (0-5). Determine normal direction vector (face.normal in local space). Transform to world direction; rotate appropriate layer: For face normal direction, pick axis (x, y, z) and sign.

Determine layer: For example clicking a face whose normal is +X (right). Then we need to rotate the layer of cubies where x coordinate == +1 (the right slice). Direction: rotate clockwise when looking at that face from outside. We'll define rotation direction based on normal and maybe mouse button.

Implement rotation animation: Create a group, add cubies belonging to layer, then animate group's rotation around appropriate axis 90deg (Math.PI/2) over, say, 300ms using requestAnimationFrame.

After animation, remove group, apply final transforms to cubies (bake matrix), and update their positions.

Simplify: Use cubie objects stored with reference to their position index (x,y,z) not used after rotation; after each rotation, we may need to update positions and maybe not maintain a logical puzzle state (just visual). That's fine.

Scramble button: On click, generate e.g., 20 random face rotations. We'll queue them sequentially with animation.

Add simple UI: button at top.

Add style: canvas full size.

Now implement code.

Let's write index.html content.