Toratopes
Can be found here: http://hi.gher.space/wiki/List_of_toratopes
- 2D
Circle - Circ
3D
Sphere - Sphe
Cylinder - Cylin
Torus - Tor
4D
Glome - Glome
Cubinder - Cubin
Spheritorus - Sphetor
Duocylinder - Docylin
Tiger - Tige
Spherinder - Spherin
Torisphere - Torsph
Torinder - Torer
Ditorus - Ditor
5D
Pentasphere - Pesphe
Tesserinder - Tessin
Toratesserinder - Torat
Duocyldyinder - Docyer
Toraduocyldyinder - Tocydi
Cubspherinder - Cusphin
Toracubspherinder - Tocubsphe
Cubtorinder - Cutrin
Toracubtorinder - Tocubit
Cylspherinder - Cysph
Cylspherintigroid - Cyspheg
Cyltorinder - Cytord
Cyltorintigroid - Cytorg
Glominder - Glomer
Toracubdyinder - Tocubdy
Cylindrical ditorus - Cydit
Tigric prism - Tigep
Tigric torus - Tigor
Toraspheridyinder - Torsphidyer
Spheric ditorus - Sphedit
Ditorinder - Ditorder
Tritorus - Tritor
Skew Apeirohedra
Can be found here: https://en.wikipedia.org/wiki/Skew_apeirohedron
- Petrie
Mucube - Mucube
Muoctahedron - Muoct
Mutetrahedron - Mutet
Gott
{4,5} 1, Mutricube - Muticub
{4,5} 2, Muoctahedron with hexagonal prisms - Muoctig
{3,7}, Muoctaicosahedron - Muoctike
{3,8} 1, Mutetraoctahedron - Mutetoct
{3,8} 2, Snub Mucube - Musnic
{3,9}, Muicosaoctahedron - Muikoct
{3,12}, Muquadrioctahedron - Muqoct
Other uniform
4.4.6.6 1 - Mugircoct
6.6.8.8 - Mucutet
4.4.4.6 - Mugirhip
4.8.4.8 - Muhigirco
3.3.3.3.3.3.3 - Muioct
4.4.4.6 - Mugirhe
4.4.4.8 - Muocube
3.4.4.4.4 - Musirco
4.4.4.4.4 - Musquip
4.4.4.6 - Muhip
Stacks
Uniform Boerdijk–Coxeter helix - Bocolix
Stack of cubes - Stac
Other rotopes
Can be found here: http://hi.gher.space/wiki/List_of_rotopes
- Bicylinder, Crind - Crin
Tricylinder, Trind - Trin
Cone - Cone
Bicone - Bico
Other polytopes
Some can be found here: https://bendwavy.org/klitzing/explain/_ ... d-ones.htm
- Expanded dodeca-augmented great rhombicuboctahedron - Exdaugirco
Rhombi-propello-icosahedron - Rhoprike
Triaconta-augmented rhombicosidodecahedron - Trisirco
p12-h4 - Trutdu
Chamfered Tetrahedron - Chatet
Chamfered Cube - Chube
Chamfered Octahedron - Choct
Chamfered Dodecahedron - Chadoe
Chamfered Icosahedron - Chike
Hopf Polyhedra
Explanation here: http://www.polytope.net/hedrondude/twisters.htm
- Hopf Tetrahedron - Hoftet
Hopf Cube - Hofube
Hopf Octahedron - Hofoc
Hopf Dodecahedron - Hodoe
Hopf Icosahedron - Hoike
Non-regular versions of regulars or uniform polytopes with different symmetries
- Tetratetrahedron - Tatet
Snub tetrahedron - Snat
Catalan dodecahedron (dual of Snat)- Catadoe
Catalan cube (dual of Tatet) - Catacube
Truncated triangle - Trit
Truncated square - Tasq
Snub square - Snasq
Rhombic square - Rasq
Tetrahedral cuboctahedron / Tritruncated tetrahedron/Rhombitetratetrahedron - Rhotet
Tetrahedral truncated octahedron / Cantitruncated tetrahedron / Bevelled tetrahedron - Cantet
Tetrahedral icosahedron - Tike
Pyritohedron - Pyrdoe
Polygon Compounds
It is a combination of a number prefix and the acronym for the said polygon.
For example, tritrig is a compound of 3 triangles and disquare is the compound of 2 octagons. After tri, we have different prefixes.
Here they are
- 2 - Di
3 - Tri
4 - Qi
5 - Pei
6 - Sei
7 - Hei
8 - Oei
9 - Noi
10 - Doi
For example, a compound of 27 squares is heidisquare.
Stellations
First take an already existing acronym. Then you put this before it {xy[sup]}. x represents the number of stellations. 1 means no stellation. The [sup]y[sup] represents the order of stellation. Here's how it works.
1 - Stellating: Replaces edges with larger edges in the same line.
2 - Greatening: Replaces faces with larger faces in the same plane.
3 - Aggrandizing: Replaces cells with larger cells in the same realm.
And so on.
Here are a few examples.
[list]
Great dodecahedron - {2[sup]2[/sup}doe
Escher solid - {2[sup]1}rad
Tetrahemihexacron - {21}cube
Conjugation
This is simple. Cu means conjugation. e.g. cu teddi is targi