diff --git a/src/lib/core/cube.ts b/src/lib/core/cube.ts
new file mode 100644
index 0000000..a116492
--- /dev/null
+++ b/src/lib/core/cube.ts
@@ -0,0 +1,11 @@
+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;
+}
diff --git a/src/lib/core/cubeindex.ts b/src/lib/core/cubeindex.ts
new file mode 100644
index 0000000..d998b4f
--- /dev/null
+++ b/src/lib/core/cubeindex.ts
@@ -0,0 +1,36 @@
+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;
+  }
+}
diff --git a/src/lib/core/cubeop.ts b/src/lib/core/cubeop.ts
new file mode 100644
index 0000000..49a720e
--- /dev/null
+++ b/src/lib/core/cubeop.ts
@@ -0,0 +1,6 @@
+import { CubeIndex } from "./cubeindex";
+
+export interface CubeOp {
+  readonly imageOf: (cubeIndex: CubeIndex, dimension: number) => CubeIndex;
+  readonly inverse: () => CubeOp;
+}