# Triangular diprism (EntityTopic, 16)

### From Hi.gher. Space

A **triangular diprism** is a special case of the prism where the base is a triangular prism. It is also a duoprism with parameters of 3 and 4.

## Equations

- Variables:

l⇒ length of each line in the triangular diprism

- The hypervolumes of a triangular diprism are given by:

total edge length = 24l

total surface area = (15 + 2√3) ·l^{2}

surcell volume = (3 + 2√3) ·l^{3}

bulk =^{√3}∕_{2}·l^{4}

- The realmic cross-sections (
*n*) of a triangular diprism are:

[!x,!y] ⇒ cuboid with a various size

[!z,!w] ⇒ triangular prism

## Net

The net of a triangular diprism is three cubes with four triangular prisms attached to the middle cube:

No image

## Projection

The parallel projection of a triangular diprism is the following:

## Incidence matrix

Dual: (dual of triangular diprism)

# | TXID | Va | Ea | Eb | 3a | 4a | 4b | C1a | C2a | Type | Name |
---|---|---|---|---|---|---|---|---|---|---|---|

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

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

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

3 | 3a | 3 | 3 | 0 | = triangle | ; joins 2 triangular prisms | |||||

4 | 4a | 4 | 0 | 4 | = square | ; joins 2 cubes | |||||

5 | 4b | 4 | 2 | 2 | = square | ; joins triangular prism to cube | |||||

6 | C1a | 6 | 6 | 3 | 2 | 0 | 3 | = base of prism: triangular prism |
; | ||

7 | C2a | 8 | 4 | 8 | 0 | 2 | 4 | = cube | ; | ||

8 | H4.1a | 12 | 12 | 12 | 4 | 3 | 12 | 4 | 3 | = triangular diprism |
; |

## Usage as facets

*prism*: 6× 1-facets of a triangular triprism

Notable Tetrashapes
| |

Regular:
| pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron |

Powertopes:
| triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate |

Circular:
| glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder |

Torii:
| tiger • torisphere • spheritorus • torinder • ditorus |

20. 21^{1}Cyltrianglinder | 21. 111
^{1}Triangular diprism | 22. 2^{2}Dicone |

List of tapertopes |