List of Rotatopes by Toratopic Notation

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

If hyperspheres are also allowed in the Cartesian products, then a larger class of polytopes known as toratopes can be constructed.

The following is a list of rotatopes, organized by their representation in toratopic notation as written by Bowers

## 0 Dimensional

* .

{\displaystyle .}

 - Point

## 1 Dimensional

{\displaystyle |}

 - Line segment

## 2 Dimensional

{\displaystyle ||}

 - Square
* (
)

{\displaystyle ()}

 - Disk

## 3 Dimensional

{\displaystyle |||}

 - Cube

(
)

{\displaystyle |()}

 - Cylinder
* (

)

{\displaystyle (|)}

 - Ball

## 4 Dimensional

 - Tesseract

(
)

{\displaystyle ||()}

 - Cubinder
* (
)
(
)

{\displaystyle ()()}

 - Duocylinder

(

)

{\displaystyle |(|)}

 - Spherinder
* (

)

{\displaystyle (||)}

 - Gongol

## 5 Dimensional

 - Penteract

(
)

{\displaystyle |||()}

 - Tessinder

(
)
(
)

{\displaystyle |()()}

 - Duocyclinder

(

)

{\displaystyle ||(|)}

 - Spherisquare
* (
)
(

)

{\displaystyle ()(|)}

 - Cyclosphere

(

)

{\displaystyle |(||)}

 - Glominder
* (

)

{\displaystyle (|||)}

 - Pentorb

## 6 Dimensional

 - Hexeract

(
)

 - Pentinder

(
)
(
)

{\displaystyle ||()()}

 - Duocyclosquare
* (
)
(
)
(
)

{\displaystyle ()()()}

 - Triocylinder

(

)

 - Sphericube

(
)
(

)

{\displaystyle |()(|)}

 - Cylindisphere
* (

)
(

)

{\displaystyle (|)(|)}

 - Duospherinder

(

)

 - Glomosquare
* (
)
(

)

{\displaystyle ()(||)}

 - Cycloglome

(

)

 - Pentorbinder
* (

)

 - Hexorb

## 7 Dimensional

 - Hepteract

(
)

 - Hexinder

(
)
(
)

{\displaystyle |||()()}

 - Duocyclocube

(
)
(
)
(
)

{\displaystyle |()()()}

 - Triocyclinder

(

)

 - Spheritesseract

(
)
(

)

{\displaystyle ||()(|)}

 - Cubindisphere
* (
)
(
)
(

)

{\displaystyle ()()(|)}

 - Duocyclosphere

(

)
(

)

{\displaystyle |(|)(|)}

 - Duosphycinder

(

)

 - Glomocube

(
)
(

)

{\displaystyle |()(||)}

 - Cylindiglome
* (

)
(

)

{\displaystyle (|)(||)}

 - Spheriglome

(

)

 - Pentorbisquare
* (
)
(

)

{\displaystyle ()(|||)}

 - Cyclopentorb

(

)

 - Hexorbinder
* (

)

 - Heptorb

## 8 Dimensional

 - Octeract

(
)

 - Heptinder

(
)
(
)

 - Duocyclotesseract

(
)
(
)
(
)

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

 - Triocyclosquare
* (
)
(
)
(
)
(
)

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

 - Tetrocylinder

(

)

 - Spheripenteract

(
)
(

)

 - Tessindisphere

(
)
(
)
(

)

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

 - Duocyclindisphere

(

)
(

)

 - Duospherisquare
* (
)
(

)
(

)

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

 - Cycloduosphere

(

)

 - Glomotesseract

(
)
(

)

 - Cubindiglome
* (
)
(
)
(

)

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

 - Duocycloglome

(

)
(

)

 - Spherindiglome
* (

)
(

)

 - Duoglominder

(

)

 - Pentorbicube

(
)
(

)

 - Cylindipentorb
* (

)
(

)

 - Spheripentorb

(

)

 - Hexorbisquare
* (
)
(

)

 - Cyclohexorb

(

)

 - Heptorbinder
* (

)

 - Octorb

## 9-Dimensional

 - Enneract

(
)

 - Octinder

(
)
(
)

 - Duocyclopenteract

(
)
(
)
(
)

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

 - Triocyclocube

(
)
(
)
(
)
(
)

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

 - Tetrocyclinder

(

)

 - Spherihexeract

(
)
(

)

 - Pentindisphere

(
)
(
)
(

)

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

 - Duocyclosquarisphere
* (
)
(
)
(
)
(

)

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

 - Triocyclosphere

(

)
(

)

 - Duosphericube

(
)
(

)
(

)

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

 - Cylindiduosphere
* (

)
(

)
(

)

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

 - Trispherinder

(

)

 - Glomopenteract

(
)
(

)

 - Tessindiglome

(
)
(
)
(

)

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

 - Duocyclindiglome

(

)
(

)

 - Spherisquariglome
* (
)
(

)
(

)

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

 - Cyclospheriglome

(

)
(

)

 - Duoglycinder

(

)

 - Pentorbitesseract

(
)
(

)

 - Cubindipentorb
* (
)
(
)
(

)

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

 - Duocyclopentorb

(

)
(

)

 - Spherindipentorb
* (

)
(

)

 - Glomopentorb

(

)

 - Hexorbicube

(
)
(

)

 - Cylindihexorb
* (

)
(

)

 - Spherihexorb

(

)

 - Heptorbisquare
* (
)
(

)

 - Cyclohexorb

(

)

 - Octorbinder
* (

)

 - Enneorb