# Magic Puzzle Ultimate¶

Magic Puzzle Ultimate (MPU or MPUlt) is a higher-dimensional puzzle simulator developed by Andrey Astrelin that can simulate nearly any symmetric doctrinaire puzzle and supports, including user-defined ones.

32-cell puzzle in MPU

## Records¶

Some records for the shortest and first solutions of a puzzle are kept on the Superliminal Wiki page.

## Virtual Puzzles¶

While we’re waiting for Hyperspeedcube 2.0 to release, Magic Puzzle Ultimate is a great program to get your feet wet in the world of other 4D puzzles.

Open the location where your MPUlt folder is. Next, open the MPUlt_puzzles.txt file. This file is a big list of all the puzzles in the program. Now you can copy & paste the puzzles that you want below under their appropriate Block. Just save the file, reopen MPUlt, and the puzzle you added will be in the menu.

### Puzzle Definitions¶

3D Puzzles
3x3x3
3x3x3
Puzzle 3x3x3
Dim 3
NAxis 1
Faces 1,0,0
Group 1,0,0/1,1,0 1,0,0/1,0,1
Axis 1,0,0
Twists 0,1,0/0,1,1
Cuts -0.33 0.33

Skewb
Skewb
Puzzle Skewb
Dim 3
NAxis 1
Faces 1,0,0
Group 1,0,0/1,1,0 1,0,0/1,0,1
Axis 1,1,1
Twists 1,-1,0/1,0,-1
Cuts 0

Compy Rainbow
Compy Rainbow
Puzzle Compy_Rainbow
Dim 3
NAxis 1
Faces 1,0,0 0.6667,0.6667,0.6667
Group 1,0,0/1,1,0 1,0,0/1,0,1
Axis 1,1,1
Twists 1,-1,0/1,0,-1
Cuts -0.45 0.45

Cuboctahedron
Cuboctahedron
Puzzle Cuboctahedron
Dim 3
NAxis 2
Faces 1,0,0 0.667,0.667,0.667
Group 1,0,0/1,1,0 1,0,0/1,0,1
Axis 1,0,0
Twists 0,1,0/0,1,1
Cuts 0.5 -0.5
Axis 1,1,1
Twists 1,-1,0/1,0,-1
Cuts 0.5 -0.5

4D Puzzles
Tesseract Family
2x2x1x1
2x2x1x1
Puzzle 2x2x1x1
Dim 0
NAxis 2
Faces 1,0,0,0 0,0,0,0.5
Group 1,0,0,0/1,1,0,0 1,0,0,0/0,0,1,0 1,0,0,0/0,0,0,1 0,1,0,0/0,0,1,0 0,1,0,0/0,0,0,1 0,0,1,0/0,0,1,1

2x2x2x1
2x2x2x1
Puzzle 2x2x2x1
Dim 4
NAxis 2
Faces 1,0,0,0 0,0,0,0.5
Group 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0 1,0,0,0/0,0,0,1
Axis 1,0,0,0
Twists 0,1,0,0/0,1,1,0 0,1,0,0/0,0,0,1
Cuts 0 0
Axis 0,0,0,1
Twists 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0
Cuts

2x2x2x3
2x2x2x3
Puzzle 2x2x2x3
Dim 4
NAxis 2
Faces 1,0,0,0 0,0,0,1.5
Group 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0 1,0,0,0/0,0,0,1
Axis 1,0,0,0
Twists 0,1,0,0/0,1,1,0 0,1,0,0/0,0,0,1
Cuts 0
Axis 0,0,0,1
Twists 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0
Cuts 0.5 -0.5

2x2x3x3
2x2x3x3
Puzzle 2x2x3x3
Dim 4
NAxis 2
Faces 1,0,0,0 0,0,1.5,0
Group 1,0,0,0/1,1,0,0 1,0,0,0/0,0,1,0 0,0,1,0/0,0,1,1
Axis 1,0,0,0
Twists 0,0,1,0/0,0,1,1 0,1,0,0/0,0,1,0 0,1,0,0/0,0,1,1
Cuts 0
Axis 0,0,1,0
Twists 1,0,0,0/1,1,0,0 0,0,0,1/1,0,0,0 0,0,0,1/1,1,0,0
Cuts 0.5 -0.5

2x2x3x4
2x2x3x4
Puzzle 2x2x3x4
Dim 4
NAxis 3
Faces 1,0,0,0 0,0,1.5,0 0,0,0,2
Group 1,0,0,0/1,1,0,0 1,0,0,0/0,0,1,0 1,0,0,0/0,0,0,1
Axis 1,0,0,0
Twists 0,1,0,0/0,0,1,0 0,1,0,0/0,0,0,1 0,0,1,0/0,0,0,1
Cuts 0
Axis 0,0,1,0
Twists 1,0,0,0/1,1,0,0 1,0,0,0/0,0,0,1 0,0,0,1/0,1,0,0
Cuts 0.5 -0.5
Axis 0,0,0,1
Twists 1,0,0,0/1,1,0,0 1,0,0,0/0,0,1,0 0,0,1,0/0,1,0,0
Cuts 1 0 -1

2x3x4x5
2x3x4x5
Puzzle 2x3x4x5
Dim 4
NAxis 4
Faces 1,0,0,0 0,1.5,0,0 0,0,2,0 0,0,0,2.5
Group 1,0,0,0/0,1,0,0 1,0,0,0/0,0,1,0 1,0,0,0/0,0,0,1
Axis 1,0,0,0
Twists 0,1,0,0/0,0,1,0 0,1,0,0/0,0,0,1 0,0,1,0/0,0,0,1
Cuts 0
Axis 0,1,0,0
Twists 1,0,0,0/0,0,1,0 1,0,0,0/0,0,0,1 0,0,1,0/0,0,0,1
Cuts 0.5 -0.5
Axis 0,0,1,0
Twists 1,0,0,0/0,1,0,0 1,0,0,0/0,0,0,1 0,0,0,1/0,1,0,0
Cuts 1 0 -1
Axis 0,0,0,1
Twists 1,0,0,0/0,1,0,0 1,0,0,0/0,0,1,0 0,0,1,0/0,1,0,0
Cuts 1.5 0.5 -0.5 -1.5

3x3x3x1
3x3x3x1
Puzzle 3x3x3x1
Dim 4
NAxis 2
Faces 1.5,0,0,0 0,0,0,0.5
Group 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0 1,0,0,0/0,0,0,1
Axis 1,0,0,0
Twists 0,1,0,0/0,1,1,0 0,1,0,0/0,0,0,1
Cuts 0.5 -0.5
Axis 0,0,0,1
Twists 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0
Cuts

3x3x3x2
3x3x3x2
Puzzle 3x3x3x2
Dim 4
NAxis 2
Faces 1.5,0,0,0 0,0,0,1
Group 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0 1,0,0,0/0,0,0,1
Axis 1,0,0,0
Twists 0,1,0,0/0,1,1,0 0,1,0,0/0,0,0,1
Cuts -0.5 0.5
Axis 0,0,0,1
Twists 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0
Cuts 0

4x4x4x4
4x4x4x4
Puzzle 4^4
Dim 4
NAxis 1
Faces 1,0,0,0
Group 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0 1,0,0,0/1,0,0,1
Axis 1,0,0,0
Twists 0,1,0,0/0,1,1,0 0,1,-1,0/0,0,0,1 0,2,-1,-1/0,1,1,-2
Cuts 0.5 0 -0.5

Other
{4}x{4} 3
{4}x{4} 3
Puzzle {4}x{4} 3
Dim 4
NAxis 2
Faces 1,0,0,0 0,0,1,0
Group 1,0,0,0/1,1,0,0 1,0,0,0/0,0,1,0 0,0,1,0/0,0,1,1
Axis 1,0,0,0
Twists 0,1,0,0/0,0,1,0 0,0,1,0/0,0,1,1
Cuts 0.5 -0.5
Axis 0,0,1,0
Twists 1,0,0,0/1,1,0,0 1,0,0,0/0,0,0,1
Cuts 0.5 -0.5

3^4 Skewb
3^4 Skewb
Puzzle 3^4 Skewb
Dim 4
NAxis 1
Faces 1,0,0,0
Simplified
Group 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0 1,0,0,0/1,0,0,1
Axis 1,1,1,1
Twists 0,2,-1,-1/0,1,1,-2 1,-1,0,0/0,0,1,-1
Cuts 0

5-5_Duotegum
5-5_Duotegum
Puzzle 5-5_Duotegum
Dim 4
NAxis 1
Faces -1,1,0,0
Group 1,0,0,0/0.809016994,0,0.587785252,0 1,1,0,0/0,0,1,1
Axis -1,1,0,0
Twists 0,0,1,0/0,0,0,1 1,1,0,0/0,0,1,1 1,1,0,0/0,0,-1,1
Cuts 0.65

16-cell Face Turning
16-cell Face Turning
Puzzle 16-cell_FT
Dim 4
NAxis 1
Faces 1,1,1,1
Group 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0 1,0,0,0/1,0,0,1
Axis 1,1,1,1
Twists 0,2,-1,-1/0,1,1,-2 1,-1,0,0/0,0,1,-1
Cuts 0.6 -0.6

Chamfered Pentagonal Duoprism
Chamfered Pentagonal Duoprism
Puzzle Chamfered_Pentagonal_Duoprism
Dim 4
NAxis 2
Faces -1.41429,0,0,0 1.41429,0,0,0 -1,1,0,0
Group 1,0,0,0/0.809016994,0,0.587785252,0 1,1,0,0/0,0,1,1
Axis -1,0,0,0
Twists 0,1,0,0/0,0.809016994,0,0.587785252 0,0,1,0/0,0,0,1
Cuts 1.3 -1.23
Axis -1,1,0,0
Twists 0,0,1,0/0,0,0,1 1,1,0,0/0,0,1,1 1,1,0,0/0,0,-1,1
Cuts 0.85

Chamefered Tesseract
Chamfered Tesseract
Puzzle Chamfered_Tesseract
Dim 4
NAxis 2
Faces 1,0,0,0 0.70710678,0.70710678,0,0
Group 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0 1,0,0,0/1,0,0,1
Axis 1,0,0,0
Twists 0,1,0,0/0,1,1,0 0,1,0,0/0,1,0,1 0,0,1,0/0,0,1,1
Cuts 0.85 -0.85
Axis 1,1,0,0
Twists 0,0,1,0/0,0,1,1 1,-1,0,0/0,0,1,0 1,-1,0,0/0,0,1,1
Cuts 0.57 -0.57

Octahedral Prism
Octahedral Prism
Puzzle Octahedral_Prism
Dim 4
NAxis 2
Faces 1,0,0,0 0,1,1,1
Group 1,0,0,0/0,1,0,0 0,1,0,0/0,1,1,0 0,1,0,0/0,1,0,1
Axis 1,0,0,0
Twists 0,1,0,0/0,1,1,0 0,1,1,0/0,0,1,1 0,1,0,0/0,0,1,1
Cuts 0.5 -0.5
Axis 0,1,1,1
Twists 0,1,-1,0/0,1,0,-1 1,0,0,0/0,1,-1,0
Cuts 0.5 -0.5

Snub 24-cell
Snub 24-cell
Puzzle Snub24cell
Dim 4
NAxis 2
Faces 1,0,0,0 0.809017,0.809017,0,0 0.9045085,0.6545085,0.25,0
#Faces 1,0,0,0 0.809017,0.809017,0,0 0.9045085,0.6545085,0.25,0 0.9045085,0.6545085,-0.25,0
Group 0,2,-1,-1/0,1,1,-2 0,1,1,2/0,2,-1,1 2,-2,-2,0/1,-1,-1,3
Axis 1,0,0,0
Twists 0,2,-1,-1/0,1,1,-2 0,0,1,0/0,0,0,1 0,1,1,2/0,2,-1,1
Cuts 0.9 -0.9
Axis 0.809017,0.809017,0,0
Twists 2,-2,-2,0/1,-1,-1,3 1,-1,-1,-3/2,-2,-2,0 0,0,0,1/0,0,1,0
Cuts 0.95 -0.95

Square Antiprism Prism
Square Antiprism Prism
Puzzle Square_Antiprism_Prism
Dim 4
NAxis 3
Faces -0.5,0,0,0 0,0,0.42044820,0 0,0.56903559,0.14014940,0
Group 0,0,1,0/0,0.38268343,0,0.92387953 0,0,0,1/0,1,0,1 1,0,0,0/0,0,0,1
Axis 1,0,0,0
Twists 0,1,0,0/0,1,0,1 0,0,1,0/0,0.38268343,0,0.92387953 0,0,1,0/0,-0.38268343,0,0.92387953
Cuts 0.1666 -0.1666
Axis 0,0,1,0
Twists 0,1,0,0/0,1,0,1 1,0,0,0/0,1,0,0 1,0,0,0/0,1,0,1
Cuts 0.1235 -0.1235
Axis 0,0.56903559,0.14014940,0
Twists 1,0,0,0/0,0,0,1
Cuts 0.621

Triangular Antitegmatic Icoschoron
Triangular Antitegmatic Icosachoron
Puzzle Triangular-antitegmatic_Icosachoron
Dim 4
NAxis 1
Faces 1,0,0,0
Group 1,0,0,0/0.5,0.866025404,0,0 0,0.577350269,0.816496581,0/0,0,0.612372436,0.790569415
#1,0,0,0/0.5,sqrt(3)/2,0,0 0,1/sqrt(3),sqrt(2/3),0/0,0,1/sqrt(6),sqrt(5/6)
Axis 1,0,0,0
Twists 0,0.577350269,0.816496581,0/0,0,0.612372436,0.790569415 0,0.790569,-0.559017,0.25/0,0.57735,1.22474,0.912871
Cuts 0.75 -0.75

5D Puzzles
Penteract Family
1x1x1x1x2
1x1x1x1x2
Puzzle 1x1x1x1x2
Dim 5
NAxis 2
Faces 0.5,0,0,0,0 0,0,0,0,1
Group 1,0,0,0,0/1,1,0,0,0 1,0,0,0,0/1,0,1,0,0 1,0,0,0,0/1,0,0,1,0 1,0,0,0,0/0,0,0,0,1
Axis 1,0,0,0,0
Twists 0,1,0,0,0/0,1,1,0,0 0,1,0,0,0/0,0,0,0,1
Cuts
Axis 0,0,0,0,1
Twists 1,0,0,0,0/1,1,0,0,0
Cuts 0

1x1x1x2x2
1x1x1x2x2
Puzzle 1x1x1x2x2
Dim 5
NAxis 2
Faces 0.5,0,0,0,0 0,0,0,1,0
Group 1,0,0,0,0/1,1,0,0,0 1,0,0,0,0/1,0,1,0,0 1,0,0,0,0/0,0,0,1,0 0,0,0,1,0/0,0,0,1,1
Axis 1,0,0,0,0
Twists 0,1,0,0,0/0,1,1,0,0 0,1,0,0,0/0,0,0,1,0 0,0,0,1,0/0,0,0,1,1
Cuts
Axis 0,0,0,1,0
Twists 1,0,0,0,0/1,1,0,0,0 1,0,0,0,0/1,0,1,0,0 1,0,0,0,0/0,0,0,0,1
Cuts 0

1x1x2x2x2
1x1x2x2x2
Puzzle 1x1x2x2x2
Dim 5
NAxis 2
Faces 0.5,0,0,0,0 0,0,1,0,0
Group 1,0,0,0,0/1,1,0,0,0 1,0,0,0,0/0,0,1,0,0 0,0,1,0,0/0,0,1,1,0 0,0,1,0,0/0,0,1,0,1
Axis 1,0,0,0,0
Twists 0,1,0,0,0/0,0,1,0,0 0,0,1,0,0/0,0,1,1,0
Cuts
Axis 0,0,1,0,0
Twists 1,0,0,0,0/1,1,0,0,0 1,0,0,0,0/0,0,0,1,0 0,0,0,1,0/0,0,0,1,1
Cuts 0

1x2x2x2x2
1x2x2x2x2
Puzzle 1x2x2x2x2
Dim 5
NAxis 2
Faces 0.5,0,0,0,0 0,1,0,0,0
Group 1,0,0,0,0/0,1,0,0,0 0,1,0,0,0/0,1,1,0,0 0,1,0,0,0/0,1,0,1,0 0,1,0,0,0/0,1,0,0,1
Axis 1,0,0,0,0
Twists 0,1,0,0,0/0,1,1,0,0
Cuts
Axis 0,1,0,0,0
Twists 1,0,0,0,0/0,0,1,0,0 0,0,1,0,0/0,0,1,1,0
Cuts 0

2x2x2x2x2
2x2x2x2x2
Puzzle 2^5
Dim 5
NAxis 1
Faces 1,0,0,0,0
Group 1,0,0,0,0/1,1,0,0,0 1,0,0,0,0/1,0,1,0,0 1,0,0,0,0/1,0,0,1,0 1,0,0,0,0/1,0,0,0,1
Axis 1,0,0,0,0
Twists 0,1,0,0,0/0,1,1,0,0
Cuts 0

Other
Simplex Prism
Simplex Prism
Puzzle Simplex_Prism
Dim 5
NAxis 2
Faces 0,0,0,0,1 1,0,0,0,0
Group 1,0,0,0,0 0,0,1,1,0/0,0,1,-1,0 0,2,-1,-1,0/0,1,1,-2,0 0,2,-2,0,0/0,1,1,-1,-2.236068
Axis 0,0,0,0,1
Twists 1,0,0,0,0/0,1,-1,0,0 0,0,1,1,0/0,0,1,-1,0 0,2,-1,-1,0/0,1,1,-2,0
Cuts 0
Axis 1,0,0,0,0
Twists 0,2,-1,-1,0/0,1,1,-2,0
Cuts 0

{3,3}x{4}
{3,3}x{4}
Puzzle {3,3}x{4}
Dim 5
NAxis 2
Faces 1,1,1,0,0 0,0,0,1.73205081,0
Group 1,1,0,0,0/1,0,-1,0,0 1,1,0,0,0/0,1,-1,0,0 0,0,0,1,0/0,0,0,1,1
Axis 1,1,1,0,0
Twists 0,0,0,1,0/0,0,0,1,1 1,-1,0,0,0/1,0,-1,0,0 1,-1,0,0,0/0,0,0,1,0
Cuts -0.33333
Axis 0,0,0,1,0
Twists 1,1,0,0,0/1,0,-1,0,0 0,0,0,0,1/1,-1,0,0,0
Cuts 0


If you figure out the notation, you can try adding your own puzzles. You define the symmetry group, rotational axes, cutting planes, possible twists and puzzle boundary.

For some definitions of various hypercuboids, see hypercuboids.

There is also a general formula for 4D duoprism puzzles, made by Luna:

{p}x{q}
Puzzle {p}x{q}
Dim 4
NAxis 2
Faces 1,0,0,0 0,0,1,0
Group 1,0,0,0/1,tan(pi/p),0,0 0,0,1,0/0,0,1,tan(pi/q)
Axis 1,0,0,0
Twists 0,1,0,0/0,0,0,1 0,0,1,0/0,0,1,tan(pi/q)
Cuts ...
Axis 0,0,1,0
Twists 0,0,0,1/0,1,0,0 1,0,0,0/1,tan(pi/p),0,0
Cuts ...