Basic cube representation types

src/lib/core/cube.ts

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+import { CubeIndex } from "./cubeindex";
+import { CubeOp } from "./cubeop";
+
+export type FaceletNumber = number;
+
+export interface Cube {
+  readonly dimension: number;
+  readonly positionOf: (FaceletNumber: number) => CubeIndex;
+  readonly occupantOf: (position: CubeIndex) => number;
+  readonly apply: (op: CubeOp) => Cube;
+}

src/lib/core/cubeindex.ts

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+export type SlotNumber = number;
+
+export interface CubeIndex {
+  readonly face: number;
+  readonly row: number;
+  readonly column: number;
+}
+
+export class IndexConverter {
+  readonly dimension: number;
+
+  static forDimension(dimension: number): IndexConverter {
+    return new IndexConverter(dimension);
+  }
+
+  fromSlotNumber(slotNumber: SlotNumber): CubeIndex {
+    const dimSquared = this.dimension ** 2;
+    return {
+      face: Math.trunc(slotNumber / dimSquared),
+      row: Math.trunc((slotNumber % dimSquared) / this.dimension),
+      column: slotNumber % this.dimension,
+    };
+  }
+
+  toSlotNumber(position: CubeIndex): SlotNumber {
+    return (
+      this.dimension ** 2 * position.face +
+      this.dimension * position.row +
+      position.column
+    );
+  }
+
+  private constructor(dimension: number) {
+    this.dimension = dimension;
+  }
+}

src/lib/core/cubeop.ts

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+import { CubeIndex } from "./cubeindex";
+
+export interface CubeOp {
+  readonly imageOf: (cubeIndex: CubeIndex, dimension: number) => CubeIndex;
+  readonly inverse: () => CubeOp;
+}