Pieces and patterns: corners, edges and centres

A 3×3×3 cube looks like 27 little cubes, but the middle one is a hidden mechanism. The 26 pieces you can see come in three kinds:

• 8 corners, each with 3 coloured stickers, where three faces meet
• 12 edges, each with 2 stickers, between two faces
• 6 centres, each with 1 sticker, in the middle of a face

Count the stickers to check: 8 × 3 + 12 × 2 + 6 × 1 = 24 + 24 + 6 = 54, which is 6 faces × 9 stickers.

To describe a cube you need to track two different things for each piece:

• its position: which slot it is in
• its orientation: how it is twisted in that slot

A corner can sit in its slot in 3 different orientations (a different one of its three stickers points towards the top or bottom face). An edge can sit in its slot in 2 orientations: right way round or flipped. A face turn moves pieces to new slots and can change how they are twisted. Solving the cube means getting every piece to the right slot and the right orientation.