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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.

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32-cell in MPU
32-cell puzzle in MPU

Records

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

Puzzle file format

All puzzles in MagicPuzzleUltimate are stored in MPUlt_puzzles.txt, which is in the same directory as the EXE.

Syntax

Each nonempty line is contains a statement, which consists of a command followed by any number of values. Commands and values within a statement are separated by spaces. Values may be strings (unquoted text with no spaces), numbers (floating-point), vectors (comma-separated numbers with no spaces), or transforms (slash-separated vectors with no spaces).

A transform is represented as a list of vectors, each specifying the normal vector of a mirror plane. These mirrors are composed to form arbitrary isometries that fix the origin. The vectors do not need to be normalized; e.g., 1,0,0 and 2,0,0 define equivalent transforms.

Puzzles are organized into a nested menu structure.

  • Block <string> begins a (sub)menu. It takes the name of the menu.
  • EndBlock ends a (sub)menu. It takes no values.

Puzzle definitions

  • Puzzle <string> begins a puzzle. It takes the name of the puzzle.
  • Dim <number> sets the number of dimensions.
  • NAxis <number> sets the number of axis orbits. It takes a number.
  • Faces <vector list> defines the pole vectors1 of the facets. Each vector defines an orbit by the pole of one facet in that orbit.
  • Simplified is optional and removes pieces of the puzzle that do not correspond to polytope elements.
  • Group <transform list> defines the symmetry group used for Faces, Axis, Twists, and Cuts. It takes a list of generators for the symmetry group.
  • Axis <vector> defines an axis orbit by the vector of one axis in that orbit.
  • Twists <transform list> defines the twists for an axis orbit, using the axis specified by Axis as a reference point. It takes a list of transforms, each of which defines one unique twist.
  • Cuts <number list> defines the cut depths for an axis, which are distances from the origin along the axis vector in descending order.
  • FixedMask <number> is unknown. It may have something to do with layer masks
  • A blank line ends a puzzle definition.

Axis, Twists, and Cuts must be repeated the number of times specified by NAxis.

Unknowns that other community members may know the answers to
  • What does FixedMask do?
  • Is the above description of Simplified accurate?
  • Is NAxis 0 valid?
  • Why are negative cut depths sometimes included for symmetric puzzles?
  • Do cut depths need to be sorted in descending order?
  • If the axis vector is not normalized, does that affect the cut depths?

Example puzzles

For some definitions of various hypercuboids, see hypercuboids.

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
FixedMask 2
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
FixedMask 2
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
Chamfered 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
FixedMask 2
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
FixedMask 2
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

Below is also a general formula for 4D polygonal 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 ...

  1. The pole vector of a plane is the vector from the origin to the closest point on the plane. The pole vector of a plane is normal to the plane and has magnitude equal to the distance of the plane from the origin. A plane that does not contain the origin always has a unique pole vector, and a nonzero pole vector always corresponds to a unique plane. ↩