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 {x

^{y[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}doeEscher solid - {2[sup]1}}rad

Tetrahemihexacron - {2

^{1}}cube

Conjugation

This is simple. Cu means conjugation. e.g. cu teddi is targi