List of Toratopes by Toratopic Notation

A **toratope** is a shape constructed from Cartesian products of multiple hyperballs and/or hyperspheres. This includes the hypercubes (as the products of multiple line segments), hyperballs, hyperspheres, intermediate shapes that can be considered as higher-dimensional analogues of the cylinder or torus, and hyperball or hypersphere products with no lower-dimensional analogies like the cyclosphere.

## 0 Dimensional

* .

{\displaystyle .}

 - Point

## 1 Dimensional

{\displaystyle |}

 - Point pair, Line segment

## 2 Dimensional

{\displaystyle ||}

 - Square
* (

)

{\displaystyle (||)}

 - Circle, Disk

## 3 Dimensional

{\displaystyle |||}

 - Cube
* (

)

{\displaystyle (|||)}

 - Sphere, Ball

(

)

{\displaystyle |(||)}

 - Tube, Cylinder
* (

(

)
)

{\displaystyle (|(||))}

 - Torus, Solid torus

## 4 Dimensional

 - Tesseract
* (

)

 - Glome, Gongol

(

)

 - Cubinder
* (

(

)
)

 - Spheritorus
* (

)
(

)

 - Duocylinder
* (
(

)
(

)
)

 - Tiger

(

)

 - Spherinder
* (

(

)
)

 - Torisphere
* (
(

)

)

)

 - Torinder
* (
(
(

)

)

)

 - Ditorus

## 5 Dimensional

 - Penteract
* (

)

 - Tetrasphere, Pentorb

(

)

 - Tessinder
* (

(

)
)

 - Glomitorus

(

)
(

)

 - Duocyclinder
* (

(

)
(

)
)

 - Spheritiger

(

)

 - Spherisquare
* (

(

)
)

 - Spheritorisphere

(

(

)
)

 - Torisquare
* (

(

(

)
)
)

 - Spheriditorus
* (

)
(

)

 - Cyclosphere
* (
(

)
(

)
)

 - Cylspherintigroid
* (

)
(

(

)
)

 - Cyclotorus
* (
(

)
(

(

)
)
)

 - Tigritorous

(

)

 - Glominder
* (

(

)
)

 - Toriglome

(

(

)
)

 - Spheritorinder
* (

(

(

)
)
)

 - Spheriditorus

(
(

)
(

)
)

 - Tigrinder
* (

(
(

)
(

)
)
)

 - Toritiger

(

(

)
)

 - Torispherinder
* (

(

(

)
)
)

 - Ditorisphere

(

(

(

)
)
)

 - Ditorinder
* (

(

(

(

)
)
)
)

 - Tritorus

## 6 Dimensional

 - Hexeract
* (

)

 - Pentasphere, Hexorb

(

)

 - Pentinder
* (

(

)
)

 - Pentaspheritorus

(

)
(

)

 - Duocyclosquare
* (

(

)
(

)
)

 - Glomitiger
* (

)
(

)
(

)

 - Triocylinder
* (
(

)
(

)
(

)
)

 - Triger

(

)

 - Sphericube
* (

(

)
)

 - Glomitorisphere

(

)
(

)

 - Cylindisphere
* (

(

)
(

)
)

 - Sphericylshperintigroid
* (

)
(

)

 - Duospherinder
* (
(

)
(

)
)

 - Duospherintigroid

(

)

 - Glomosquare
* (

(

)
)

 - Spheritoriglome
* (

)
(

)

 - Cycloglome
* (
(

)
(

)
)

 - Cylglomintigroid

(

)

 - Pentorbinder
* (

(

)
)

 - Toripentorb
* (
(
(

)

)

)

)

 - Toraglominder
* (
(
(
(

)

)

)

)

)

 - Tetratorus

## 7 Dimensional

 - Hepteract
* (

)

 - Hexasphere,Heptorb

(

)

 - Hexinder
* (

(

)
)

 - Torahexinder

(

)
(

)

 - Duocyclocube
* (

(

)
(

)
)

 - Toraduocyclocube

(

)
(

)
(

)

 - Triocyclinder
* (

(

)
(

)
(

)
)

 - Toratriocyclinder

(

)

 - Spheritesseract
* (

(

)
)

 - Toraspheritesseract

(

)
(

)

 - Cubindisphere
* (

(

)
(

)
)

 - Toracubindisphere
* (

)
(

)
(

)

 - Duocyclosphere
* (
(

)
(

)
(

)
)

 - Toraduocyclosphere

(

)
(

)

 - Duosphycinder
* (

(

)
(

)
)

 - Toraduosphycinder

(

)

 - Glomocube
* (

(

)
)

 - Toraglomocube

(

)
(

)

 - Cylindiglome
* (

(

)
(

)
)

 - Toracylindiglome
* (

)
(

)

{\displaystyle (|)(||)}

 - Spheriglome
* (
(

)
(

)
)

{\displaystyle ((|)(||))}

 - Toraspheriglome

(

)

 - Pentorbisquare
* (

(

)
)

 - Torapentorbisquare
* (

)
(

)

 - Cyclopentorb
* (
(

)
(

)
)

 - Toracyclopentorb

(

)

 - Hexorbinder

(

)

 - Torahexorbinder

(
(

)
(

)
(

)
)

 - Leonic prism
* (

(
(

)
(

)
(

)
)
)

 - Leonic torus
* (
(
(

)

)

)

)

)

 - Torapentorbinder
* (
(
(
(

)

)

)

)

)

)

 - Pentatorus

## 8 Dimensional

 - Octeract
* (

)

 - Heptasphere, Octorb

(

)

 - Heptinder
* (

(

)
)

 - Toraheptinder

(

)
(

)

 - Duocyclotesseract

(

)
(

)

 - Toraduocyclotesseract

(

)
(

)
(

)

 - Triocyclosquare
* (

(

)
(

)
(

)
)

 - Duotriocyclosquare
* (

)
(

)
(

)
(

)

 - Tetrocylinder
* (
(

)
(

)
(

)
(

)
)

 - Tetriger

(

)

 - Spheripenteract
* (

(

)
)

 - Toraspheripenteract

(

)
(

)

 - Tessindisphere
* (

(

)
(

)
)

 - Toratessindisphere

(

)
(

)
(

)

 - Duocyclindisphere
* (

(

)
(

)
(

)
)

 - Toraduocyclindisphere

(

)
(

)

 - Duospherisquare

(

)
(

)

 - Toraduospherisquare
* (

)
(

)
(

)

 - Cycloduosphere
* (
(

)
(

)
(

)
)

 - Toracycloduosphere
* (

)
(

)

 - Duoglominder
* (
(

)
(

)
)

 - Glomitiger

(

)

 - Glomotesseract
* (

(

)
)

 - Toralomotesseract

(

)
(

)

 - Cubindiglome
* (

(

)
(

)
)

 - Toracubindiglome
* (

)
(

)
(

)

 - Duocycloglome
* (
(

)
(

)
(

)
)

 - Toraduocycloglome

(

)
(

)

 - Spherindiglome
* (

(

)
(

)
)

 - Torapherindiglome
* (

)
(

)

 - Duoglominder
* (
(

)
(

)
)

 - Toraduoglominder

(

)

 - Pentorbicube
* (

(

)
)

 - Torapentorbicube

(

)
(

)

 - Cylindipentorb
* (

(

)
(

)
)

 - Toracylindipentorb
* (

)
(

)

 - Spheripentorb
* (
(

)
(

)
)

 - Toraspheripentorb

(

)

 - Hexorbisquare
* (

(

)
)

 - Toraexorbisquare
* (

)
(

)

 - Cyclohexorb
* (
(

)
(

)
)

 - Toracyclohexorb

(

)

 - Heptorbinder
* (

(

)
)

 - Toraheptorbinder
* (
(
(

)

)

)

)

)

)

 - Torahexorbinder
* (
(
(
(

)

)

)

)

)

)

)

 - Hexatorus

## 9-Dimensional

 - Enneract
* (

)

 - Octasphere, Enneorb

(

)

 - Octinder
* (

(

)
)

 - Toraoctinder

(

)
(

)

 - Duocyclopenteract
* (

(

)
(

)
)

 - Toraduocyclopenteract

(

)
(

)
(

)

 - Triocyclocube
* (

(

)
(

)
(

)
)

 - Toratriocyclocube

(

)
(

)
(

)
(

)

 - Tetrocyclinder
* (

(

)
(

)
(

)
(

)
)

 - Toratetrocyclinder

(

)

 - Spherihexeract
* (

(

)
)

 - Toraspherihexeract

(

)
(

)

 - Pentindisphere
* (

(

)
(

)
)

 - Torapentindisphere

(

)
(

)
(

)

 - Duocyclosquarisphere
* (

(

)
(

)
(

)
)

 - Toraduocyclosquarisphere
* (

)
(

)
(

)
(

)

 - Triocyclosphere
* (
(

)
(

)
(

)
(

)
)

 - Toratriocyclosphere

(

)
(

)

 - Duosphericube
* (

(

)
(

)
)

 - Toraduosphericube

(

)
(

)
(

)

 - Cylindiduosphere
* (

(

)
(

)
(

)
)

 - Toracylindiduosphere
* (

)
(

)
(

)

 - Trispherinder
* (
(

)
(

)
(

)
)

 - Toratrispherinder

(

)

 - Glomopenteract
* (

(

)
)

 - Toraglomopenteract

(

)
(

)

 - Tessindiglome
* (

(

)
(

)
)

 - Toratessindiglome

(

)
(

)
(

)

 - Duocyclindiglome
* (

(

)
(

)
(

)
)

 - Toraduocyclindiglome

(

)
(

)

 - Spherisquariglome
* (

(

)
(

)
)

 - Toraspherisquariglome
* (

)
(

)
(

)

 - Cyclospheriglome
* (
(

)
(

)
(

)
)

 - Toracyclospheriglome

(

)
(

)

 - Duoglycinder
* (

(

)
(

)
)

 - Toraduoglycinder

(

)

 - Pentorbitesseract
* (

(

)
)

 - Torapentorbitesseract

(

)
(

)

 - Cubindipentorb
* (

(

)
(

)
)

 - Toracubindipentorb
* (

)
(

)
(

)

 - Duocyclopentorb
* (
(

)
(

)
(

)
)

 - Toraduocyclopentorb

(

)
(

)

 - Spherindipentorb

(

)
(

)

 - Toraspherindipentorb
* (

)
(

)

 - Glomopentorb
* (
(

)
(

)
)

 - Toraglomopentorb

(

)

 - Hexorbicube
* (

(

)
)

 - Torahexorbicube

(

)
(

)

 - Cylindihexorb
* (

(

)
(

)
)

 - Toracylindihexorb
* (

)
(

)

 - Spherihexorb
* (
(

)
(

)
)

 - Toraspherihexorb

(

)

 - Heptorbisquare
* (

(

)
)

 - Toraheptorbisquare
* (

)
(

)

 - Cyclohexorb
* (
(

)
(

)
)

 - Toracyclohexorb

(

)

 - Octorbinder
* (

(

)
)

 - Toraoctorbinder

(
(

)
(

)
(

)
(

)
)

 - Oncic prism
* (

(
(

)
(

)
(

)
(

)
)
)

 - Oncic torus
* (
(
(

)

)

)

)

)

)

)

 - Toraheptorbinder
* (
(
(
(

)

)

)

)

)

)

)

)

 - Heptatorus