# Triangular triprism (EntityTopic, 13)

### From Hi.gher. Space

A **triangular triprism** is a special case of the prism where the base is a triangular diprism. It is also the Cartesian product of a triangle and a cube.

## Net

The net of a triangular diprism is three tesseracts with six triangular diprisms attached to the middle tesseract.

## Incidence matrix

Dual: (dual of triangular triprism)

# | TXID | Va | Ea | Eb | 3a | 4a | 4b | C1a | C2a | C2b | H4.1a | H4.2a | Type | Name |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | Va | = point | ; | |||||||||||

1 | Ea | 2 | = digon | ; blue | ||||||||||

2 | Eb | 2 | = digon | ; black | ||||||||||

3 | 3a | 3 | 3 | 0 | = triangle | ; joins 3 triangular prisms | ||||||||

4 | 4a | 4 | 0 | 4 | = square | ; joins base-cubes with 2 sweep-cubes | ||||||||

5 | 4b | 4 | 2 | 2 | = square | ; joins 1 triangular prism with 2 sweep-cubes | ||||||||

6 | C1a | 6 | 6 | 3 | 2 | 0 | 3 | = triangular prism | ; | |||||

7 | C2a | 8 | 0 | 12 | 0 | 6 | 0 | = cube | ; base | |||||

8 | C2b | 8 | 4 | 8 | 0 | 2 | 4 | = cube | ; sweep | |||||

9 | H4.1a | 16 | 8 | 24 | 0 | 12 | 12 | 0 | 2 | 6 | = geochoron | ; | ||

10 | H4.2a | 12 | 12 | 12 | 4 | 3 | 12 | 4 | 0 | 3 | = base of prism: triangular diprism |
; | ||

11 | H5.1a | 24 | 24 | 36 | 8 | 18 | 36 | 12 | 3 | 18 | 3 | 6 | = triangular triprism |
; |

## Usage as facets

*This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.*

Notable Pentashapes
| |

Flat:
| pyroteron • aeroteron • geoteron |

Curved:
| tritorus • pentasphere • glone • cylspherinder • tesserinder |

43. 211^{1}Cyltriandyinder | 44. 1111
^{1}Triangular triprism | 45. 3^{2}Disphone |

List of tapertopes |