# Tymon’s 1x3x3x3¶

Tymon’s 1x3x3x3

4D Shape: Hypercuboid

Physical Shape: Cube

Pieces: 8 5c, 12 4c, 6 3c, 1 2c (2 1c)

Magnets: 936

Completed: 2024 Jan 26

## History¶

Two days after finishing the 1x2x3x3 Tymon F completed his final goal, creating a physical analog of the 1x3x3x3 puzzle. To do this he had to assemble another four 4c pieces, four 3c pieces and one 2c piece that represents two 1c pieces on the virtual puzzle. This ended Tymon’s journey of creating all physical puzzles from the AxBxCx1 family.

## Moves¶

Legal moves of a layer include 90° twists, 180° twists in any plane, or a combination of both.

## Solving¶

Every piece on the puzzle has pink and purple stickers which indicate which 4d orientation the piece is. In the solved state every piece must have the same 4d axis orientation. 1x3x3x3 is harder than the 3d Rubik’s cube, but it can be solved by: orienting 3c pieces in 4d axis, orienting 4c pieces in 4d axis, orienting 5c pieces in 4d axis, except “OLL parity” (because of the extra axis, a single 5c can be missoriented), then solving the rest of the puzzle like a 3d Rubik’s cube. Tymon made a YouTube video explaining the puzzle as well as showing an example solve.

### Gyro¶

This puzzle has two 1c pieces that are physicaly represented by one 2c piece (the core). Technically the puzzle is solved only when all of the other pieces have the pink sticker on the outside cell (because pink is outside on the core piece). To be able to solve the puzzle with purple color facing outwards, Tymon created a gyro algorithm that flips all pieces inside out and puts the core outside of the puzzle. This represents that pink/purple axis is flipped and now the puzzle is only solved when all of the pieces are oriented with purple on the ouside. The gyro can be reversed to get back to default projection.

### OLL Parity¶

Becuase of the extra freedom of the 4th dimension a monoflip (single missoriented corner) can occur. It can be solved by doing one of the 4d moves, to set up a valid OLL case or just rotate corners and undoing 4d move. A single corner can also be rotated with a simple commutator.

### Alternative Solved state¶

The original solved state well represents which sticker on a piece is on the inside and which one is on the outside, but some people prefer a solved state with edges rotated 4 dimensionaly. This is because then the overall look of the puzzle is less chaotic and more friendly to non hypercubers.