# Tetrahedral prism (EntityTopic, 21)

### From Hi.gher. Space

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- | {{Shape|Tetrahedral prism| | + | <[#ontology [kind topic] [cats Uniform Prism Tapertope Bicupolic_ring]]> |

+ | {{STS Shape | ||

+ | | image=<[#embed [hash 2Y6EC6FJBFXCPWWPHGZ9G626QE] [width 120]]> | ||

+ | | name=Tetrahedral prism | ||

+ | | dim=4 | ||

+ | | elements=6, 15, 16, 8 | ||

+ | | genus=1 | ||

+ | | ssc=[xG3P] | ||

+ | | ssc2=+Kt1 | ||

+ | | extra={{STS Tapertope | ||

+ | | order=2, 2 | ||

+ | | notation=11<sup>2</sup> | ||

+ | | index=26 | ||

+ | }}{{STS Polytope | ||

+ | | dual=[[Tetrahedral bipyramid]] | ||

+ | | flayout={{FLD|dim=4|left=erev2|a3|line|a3|line2|a2tend2|end|e3}} | ||

+ | | bowers=Tepe | ||

+ | }}{{STS Uniform polytope | ||

+ | | vlayout=([[Triangle|3]][[Tetrahedron|<sup>3</sup>]])⋅([[Triangle|3]]⋅[[Square|4]]<sup>2</sup>)<sup>3</sup> | ||

+ | | vfigure=[[Tetrahedron]] | ||

+ | }}}} | ||

+ | The '''tetrahedral prism''' is a special case of a [[prism]] where the base is a [[tetrahedron]]. It is also the ''[[Bicupolic ring|digonal orthobicupolic ring]]''.[http://teamikaria.com/hddb/forum/viewtopic.php?p=20174#p20174] It is bounded by two tetrahedra and four triangular prisms. | ||

- | + | == Projections == | |

+ | <[#embed [hash DBV3TEA1JZA5TJRGC1AHJBNWF2]]> | ||

+ | |||

+ | <[#polytope [id 132]]> | ||

+ | |||

+ | == Software models == | ||

+ | *[[Polyview]] [http://hddb.teamikaria.com/dl/ED8QPT5FPREVRS12QPT8JEDMVM.def .def file] | ||

+ | *[[Stella4D]] [http://hddb.teamikaria.com/dl/GZ0E6ETAVN7SG02GPPB6JCBM3M.off .off file] | ||

{{Tetrashapes}} | {{Tetrashapes}} | ||

- | {{ | + | {{Tapertope Nav|25|26|27|1[11]<sup>1</sup><br>Square pyramid prism|11<sup>2</sup><br>Tetrahedral prism|[11<sup>1</sup>]<sup>1</sup><br>Triangular prismic pyramid|chora}} |

## Latest revision as of 17:49, 19 September 2017

The **tetrahedral prism** is a special case of a prism where the base is a tetrahedron. It is also the *digonal orthobicupolic ring*.[1] It is bounded by two tetrahedra and four triangular prisms.

## Projections

## Incidence matrix

Dual: tetrahedral bipyramid

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

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

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

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

3 | 4a | 4 | 2 | 2 | = square | ; | ||||

4 | 3a | 3 | 0 | 3 | = triangle | ; | ||||

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

6 | C2a | 4 | 0 | 6 | 0 | 4 | = base of prism: tetrahedron |
; | ||

7 | H4.1a | 8 | 4 | 12 | 6 | 8 | 4 | 2 | = tetrahedral prism |
; |

## Usage as facets

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

## Software models

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 |

25. 1[11]^{1}Square pyramid prism | 26. 11
^{2}Tetrahedral prism | 27. [11^{1}]^{1}Triangular prismic pyramid |

List of tapertopes |