Four Dimensional Dice Up To Twenty Sides


This page will reveal all known polychoric dice up to twenty sides. All of the cells of each of these polychora are congruent. Most of these have never been displayed or even listed anywhere to my knowledge. The pictures were done with Stella4D and show a projection, the cell, and the net of each dice.

5 Sides


Pentachoron

Pentachoron

The pentachoron is a regular polychoron with 5 sides and is the 4-D version of the tetrahedron. It can also be created as a gyrochoron, it is the 5-2 gyro. It is an odd die, meaning that a vertex is opposite to a facet, so it lands corner up. It also has variants as does most dice. Variants of the pentachoron has a skew-pentagon symmetry.


6 Sides


Squared Trigon

Triddip

Triddip can also be called the "squared trigon" or "squared triangle" since it is the cross product of two triangles. It has 6 sides and is uniform. This die is a wedge die since a ridge (2-D face) will face up when it sits on a table. It is also the 6-2 gyro.


7 Sides


Mobius 7

Mobius 7

The heptachoron or as I like to call it, Mobius 7, is the gyrochoron 7-2 and is also the 7-3 gyro. It has 7 sides. It is a skew die for when it sits on a 4-D table, it seems a bit skewed.


8 Sides


Tesseract

Tesseract

The tesseract is the famous hypercube. It is a regular polychoron with 8 sides and is the 4-D version of the cube. It can also be created as a gyrochoron, it is the 8-3 gyro. It is an even die, meaning that a facet is opposite to a facet, so it lands cell up. It can also be called the squared square. It also has variants as does most dice.


Tetrahedron Gem

Tet Gem

The tetrahedron gem, aka tet gem or tet tegum, is the dual of the tet prism (tepe). It has 8 sides. It can be a wedge die or a sloped wedge die, with an edge opposite the facet, usually at a slope.


Mobius 8

Mobius 8

Mobius 8 is the gyrochoron 8-2. It has 8 sides. It is also a skew die.


9 Sides


Trigon Diamond

Trigon Diamond

The trigon diamond, aka the triangular duotegum is the dual of the triangular duoprism (triddip). It has 9 sides. It is a wedge die, with an edge opposite the facet.


Mobius 9

Mobius 9

Mobius 9 is the gyrochoron 9-2. It is also the 9-4 gyro. It has 9 sides and is a wedge die with a kite shaped face pointing up.


Trigon Tricoil

Trigon Tricoil

The trigon tricoil is the gyrochoron 9-3. It sort of looks like a twisting crystal. It has 9 sides and is a sloped die with a vertex pointing up, but sloped to the side of a face.


10 Sides


Decachoron

Deca

The decachoron, aka deca is a uniform polychoron from category 7. It has 10 sides shaped like tut. It can also be created as a gyrochoron, it is the 10-3 gyro. It is an even die. It also has skewed variants.


Squared Pentagon

Pedip

The pentagon duoprism, or Pedip can also be called the "squared pentagon". It has 10 sides and is uniform. This die is a wedge die with a pentagon face pointing upwards. It is also the 10-4 gyro. A badly skewed variant is shown below.

Skewed Pedip


Gemmed 10

Gemmed 10

The gemmed decachoron is the dual of rap, aka durap. It has 10 sides shaped like trigon gems. It is a wedge die where an edge sticks up.


Mobius 10

Mobius 10

Mobius 10 is the gyrochoron 10-2. It has 10 sides and is a skew die.


11 Sides


Mobius 11

Mobius 11

Mobius 11 is the gyrochoron 11-2. It is also the 11-5 gyro. It has 11 sides and is a skew die.


Rocky 11

Rocky 11

Rocky 11 is the gyrochoron 11-3. It is also the 11-4 gyro. It can also be called the hendecachoron. It has 11 sides and is a skew die.


12 Sides


Squared Hexagon

Hiddip

The hexagon duoprism, or Hiddip can also be called the "squared hexagon". It has 12 sides and is uniform. This die is even. It is also the 12-5 gyro.


Cubic Gem

Cube Gem

The cubic gem, aka cube gem or cube tegum, is the dual of the oct prism (ope). It is an even die with 12 sides.


Trigon Square Duogem

Trigon Square Duogem

The trigon square duogem, aka triangular square duotegum is the dual of tisdip. It has 12 sides. It is a sloped die, with a sloped face opposite the facet.


Dyad Trigon Duocrystal

Dyad Trigon Duocrystal

The dyad trigon duocrystal has 12 sides. It is a sloped die, with a sloped face opposite the facet.


Mobius 12

Mobius 12

Mobius 12 is the gyrochoron 12-2. It has 12 sides and is a wedge die with a kite pointing up.


Square Tricoil

Square Tricoil

The square tricoil is the gyrochoron 12-3. It has 12 sides and is an even, yet twisty looking die.


Trigon Tetracoil

Trigon Tetracoil

The trigon tetracoil is the gyrochoron 12-4. It has 12 sides and is a sloped die with a vertex pointing up, but sloped to the side of an isosceles triangle face.


13 Sides


Mobius 13

Mobius 13

Mobius 13 is the gyrochoron 13-2, as well as the 13-6 gyro. It has 13 sides and is a skew die.


Rocky 13

Rocky 13

Rocky 13 is the gyrochoron 13-3. It is also the 13-4 gyro. It is a skew die with 13 sides.


Tridecachoron

Tridecachoron

The tridecachoron is the gyrochoron 13-5, it has twice the symmetry as the other 13 sided gyros. This 13 sided die is odd with a vertex pointing straight up. When it comes to polytope dice, 13 is the magic number - there are 13 types of polytope dice with 13 sides: one in 2-D, three in 4-D, four in 6-D, three in 8-D, one in 10-D, and one (the simplex) in 12-D. No other number appears to do this.


14 Sides


Squared Heptagon

Squared Heptagon

The heptagon duoprism, or Hedip can also be called the "squared heptagon". It has 14 sides and is uniform. This wedge die has a heptagon face pointing up. It is also the 14-6 gyro.


Mobius 14

Mobius 14

Mobius 14 is the gyrochoron 14-2. It has 14 sides and is a skew die.


Gyrus 14

Gyrus 14

Gyrus 14 is the gyrochoron 14-3. It is also the 14-5 gyro. It is an even die with 14 sides.


Rocky 14

Rocky 14

Rocky 14 is the gyrochoron 14-4. It has 14 sides. It is a sloped die with a sloped isosceles triangle pointing up.


15 Sides


Trigon Pentagon Duogem

Trigon Pentagon Duogem

The trigon pentagon duogem, aka triangular pentagonal duotegum is the dual of tipdip. It has 15 sides. It is a sloped die, with a sloped edge opposite the facet.


Mobius 15

Mobius 15

Mobius 15 is the gyrochoron 15-2, as well as the 15-7 gyro. It has 15 sides and is a wedge die with a kite shaped face pointing up. The mobius dice are looking more and more like the smoothly curved bicoiloid.


Pentagon Tricoil

Pentagon Tricoil

The pentagon tricoil is the gyrochoron 15-3. It has 15 sides and is a sloped die with a sloped hexagon ridge pointing up.


Triswirl 15

Triswirl 15

The triswirl 15 is the gyrochoron 15-4, it has double the symmetry of other 15 gyros. It has 15 sides that can split into three swirling girdles of five, making it a polyhedral version of the more curvy tridyster. It is a wedge die with a rectangular looking hexagon ridge pointing up.


Trigon Pentacoil

Trigon Pentacoil

The trigon pentacoil is the gyrochoron 15-5. It has 15 sides and is a sloped die with a vertex pointing up, but sloped to the side of a long kite shaped face.


Pentagonal Funk

Pentagonal Funk

The pentagonal funk is the gyrochoron 15-6. It has a pentagonal equator and 15 warped looking pentagonal prisms for sides that form a trifoil knot. It is a wedge die with a kite shaped ridge pointing up.


16 Sides


Hexadecachoron

Hex

The hexadecachoron, hex for short is also called the 16-cell. It is a regular polychoron with 16 sides and is the 4-D version of the octahedron. It can also be considered as the square diamond and is even.


Squared Octagon

Odip

The octagon duoprism, or Odip can also be called the "squared octagon". It has 16 sides and is uniform and even. It is also the 16-7 gyro as well as phase 3 of the 8-3 bigyro.


Square Crystal Gem

Square Crystal Gem

The square crystal gem, aka square antiduotegum is the dual of the square antiduoprism. It has 16 sides and is a sloped die with a trigon ridge pointing up.


Dyad Square Duocrystal

Dyad Square Duocrystal

The dyad square duocrystal has 16 sides. It is an even die.


Mobius 16

Mobius 16

Mobius 16 is the gyrochoron 16-2. It has 16 sides and is a skew die.


Gyrus 16

Gyrus 16

Gyrus 16 is the gyrochoron 16-3. It is also the 16-5 gyro. It is an even die with 16 sides.


Square Tetracoil

Square Tetracoil

The trigon tetracoil is the gyrochoron 16-4. It has 16 sides and is a sloped die with a vertex pointing up, but sloped to the side of an isosceles triangle ridge.


Funky 16

Funky 16

Funky 16 is the gyrochoron 16-6 and is a sort of hexagon "funk prism". Its 16 sides look like funky hexagon prisms with a couple pentagon faces. These "prisms" form a trifoil knot. It is a sloped die with a sloped pentagonal ridge pointing up.


Domed 16

Domed 16

The domed 16 is an "ionic split tesseract". It is also phase 1 of the bigyro 8-3. It is an even die with 16 sides that have a domed house shape.


Tetswirl 16

Tetswirl 16

The tetswirl 16 is a swirlprism like dice that has tetrahedral swirl symmetry with four girdles of four sides. It is also phase 2 of the bigyro 8-3. It is an even die with 16 sides.


Cracked 16

Cracked 16

The cracked 16 is phase 4 of the bigyro 8-3. It looks like a hexadecachoron after an earthquake. It is an even die with 16 sides.


Shattered 16

Shattered 16

The shattered 16 is phase 5 of the bigyro 8-3. It looks somewhat like cracked 16 and the broken tesseract. It is an even die with 16 sides.


Broken Tesseract

Broken Tesseract

The broken tesseract is phase 6 of the bigyro 8-3. It looks like a warped and cracked up tesseract. It is an even die with 16 sides.


Special 16

Special 16

The special 16 is a one hit intersection of the bigyro 8-3 where phases 1, 2, 3, and 4 meet. It is an even die with 16 sides.


Clunkeract

Clunkeract

This is the intersection of phase 1 and phase 2 of the bigyro 8-3. It is an even die with 16 sides.


Stegosaur 16

Stegosaur 16

This is the intersection of phase 2 and phase 3 of the bigyro 8-3. It is an even die with 16 sides.


Fractured 16

Fractured 16

This is the intersection of phase 3 and phase 4 of the bigyro 8-3. It is an even die with 16 sides.


Chunky 16

Chunky 16

This is the intersection of phase 1 and phase 4 of the bigyro 8-3. It is an even die with 16 sides.


Clunky 16

Clunky 16

This is the intersection of phase 2 and phase 6 of the bigyro 8-3. It is an even die with 16 sides.


Spintet 16

 16

This is the intersection of phase 5 and phase 6 of the bigyro 8-3. It is an even die with 16 sides.


Wedgy 16

Wedgy 16

This is the intersection of phase 3 and phase 5 of the bigyro 8-3. It is an even die with 16 sides.


17 Sides


Mobius 17

Mobius 17

Mobius 17 is the gyrochoron 17-2, as well as the 17-8 gyro. It has 17 sides and is a skew die.


Gyrus 17

Gyrus 17

Gyrus 17 is the gyrochoron 17-3, as well as the 17-6 gyro. It has 17 sides and is a sloped die with a sloped decagon ridge pointing up.


Rocky 17

Rocky 17

Rocky 17 is the gyrochoron 17-4, it has double symmetry. It has 17 sides and is an odd die with a vertex pointing up.


Funky 17

Funky 17

Funky 17 is the gyrochoron 17-5, as well as the 17-7 gyro. It has 17 sides and is a skew die.


18 Sides


Squared Enneagon

Squared Enneagon

The enneagon duoprism, or Edip can also be called the "squared enneagon". It has 18 sides and is uniform. This wedge die has an enneagon face pointing up. It is also the 18-8 gyro.


Trigon Hexagon Duogem

Trigon Hexagon Duogem

The trigon hexagon duogem, aka triangular hexagonal duotegum is the dual of thiddip. It has 18 sides. It is a sloped die, with a sloped triangle opposite the facet.


Trigon Duocrystal

Trigon Duocrystal

The trigon duocrystal has 18 sides. It is the dual of the trigon duoantiprism, which is not uniform. It is an even die.


Trigon Duoc

Trigon Duoc

The trigon duoc, or "duocatri" is a powertope, it is the duoc of the triangle and it has 18 sides. It is a wedge die with an edge pointing up.


Trigon Antiduoc

Trigon Antiduoc

The trigon antiduoc is related to the trigon duoc like an antiprism is related to a prism. It has 18 sides. It is a sloped die with a vertex pointed up and to the side.


Mobius 18

Mobius 18

Mobius 18 is the gyrochoron 18-2. It has 18 sides and is a wedge die with a kite shape ridge pointing up.


Hexagon Tricoil

Hexagon Tricoil

The hexagon tricoil is the gyrochoron 18-3. It has 18 sides and is an even die.


Rocky 18

Rocky 18

Rocky 18 is the gyrochoron 18-4. It has 18 sides and is a slope die with a sloped hexagonal ridge pointing up.


Triswirl 18

Triswirl 18

The triswirl 18 is the gyrochoron 18-5, it is also the 18-7 gyro. It has 18 sides that can split into three swirling girdles of six, making it a polyhedral version of the more curvy tridyster. It is an even die.


Trigon Hexacoil

Trigon Hexacoil

The trigon hexacoil is the gyrochoron 18-6. It has 18 sides and is a sloped die with a vertex pointing up, but sloped to the side of a long triangle shaped ridge.


Hexagonal Funk

Hexagonal Funk

The hexagonal funk is the gyrochoron 18-3/2. It has a hexagonal equator and 18 warped looking hexagonal prisms for sides that form a trifoil knot. It is a sloped die with a sloped triangle ridge pointing up.


19 Sides


Mobius 19

Mobius 19

Mobius 19 is the gyrochoron 19-2, as well as the 19-9 gyro. It has 19 sides and is a skew die.


Gyrus 19

Gyrus 19

Gyrus 19 is the gyrochoron 19-3, as well as the 19-6 gyro. It has 19 sides and is a sloped die with a sloped dodecagon ridge pointing up.


Rocky 19

Rocky 19

Rocky 19 is the gyrochoron 19-4, as well as the 19-5 gyro. It has 19 sides and is a sloped die with a sloped hexagon ridge pointing up.


Funky 19

Funky 19

Funky 19 is the gyrochoron 19-7, as well as the 19-8 gyro, it can also be called the heptagonal funk prism. Its 19 sides look like warped heptagonal prisms that form a trifoil knot path. It is a sloped die with a sloped kite ridge facing up.


20 Sides


Squared Decagon

Squared Decagon

The decagon duoprism, or Dedip can also be called the "squared decagon". It has 20 sides and is uniform. This die is even. It is also the 20-9 gyro and phase 3 of both the bigyro and the antibigyro 10-3.


Square Pentagon Duogem

Square Pentagon Duogem

The square pentagon duogem, aka square pentagonal duotegum is the dual of squipdip. It has 20 sides. It is a sloped die, with a sloped triangle opposite the facet.


Dyad Pentagon Duocrystal

Dyad Pentagon Duocrystal

The dyad pentagon duocrystal has 20 sides. It is a sloped die, with a sloped triangle pointing up.


Pentagon Crystal Gem

Pentagon Crystal Gem

The pentagon crystal gem, aka pentagon antiduotegum is the dual of the pentagon antiduoprism. It has 20 sides and is even.


Crystalic 20

Crystalic 20

The crystalic 20 is the dual of spid, aka "duspid". It has 20 sides that look like flattened cubes. It is even. It is also the intersection of phase 1 and 2 of the antibigyro 10-3. This shape is also the shadow of the penteract.


Mounted Pentchoron

Mounted Pentachoron

The mounted pentachoron is the dual of tip, aka "dutip". It has 20 sides and it's a sloped die which is sloped with a slanted edge pointing up.


Prismigemmed 20

Tudurap

The prismigemmed 20, aka tudurap is formed by the core of two intersected gemmed 10s (duraps). It has 20 sides and is even. It is also the intersection between phase 1 and 2 of the 10-3 bigyro.


Mobius 20

Mobius 19

Mobius 20 is the gyrochoron 20-2. It has 20 sides and is a skew die.


Gyrus 20

Gyrus 20

Gyrus 20 is the gyrochoron 20-3, as well as the 20-7 gyro. It has 20 sides and is even.


Pentagon Tetracoil

Pentagon Tetracoil

The pentagon tetracoil is the gyrochoron 20-4. It has 20 sides and is a wedge die with a kite shaped ridge pointing up.


Square Pentacoil

Square Pentacoil

The square pentacoil is the gyrochoron 20-5. It has 20 sides and is an even die.


Funky 20

Funky 20

The funky 20 is the gyrochoron 20-6. It has 20 sides and is a wedge die with a kite shaped ridge pointing up.


Double Helix 20

Double Helix 20

The double helix 20 is the gyrochoron 20-8. It has 20 sides that form two closed helixes that wrap around each other. It is a wedge die with a pentagon shaped ridge pointing up.


Rocky 20

Rocky 20

The rocky 20 is the gyrochoron 2*10-3, it is also the gyrochoron 2*10-2, and phase 1 of the antibigyro 10-3. It has 20 sides and is an even die.


Chunky 20

Chunky 20

The chunky 20 is phase 1 of the bigyro 10-3. It has 20 sides and is an even die.


Clunky 20

Clunky 20

The clunky 20 is phase 2 of the bigyro 10-3. It has 20 sides and is an even die.


Stegosaur 20

Stegosaur 20

The stegosaur 20 is the transition between phase 2 and 3 of the bigyro 10-3. It has 20 sides and is an even die.


Broken Crystalic 20

Broken Crystalic 20

The broken crystalic 20 is phase 2 of the antibigyro 10-3. It has 20 sides and is an even die.


Special 20

Special 20

The special 20 is the transition between phase 2 and 3 of the antibigyro 10-3. It has 20 sides and is an even die.


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