Tetrahedral prism (EntityTopic, 21)
From Hi.gher. Space
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| - | {{Shape | + | <[#ontology [kind topic] [cats Uniform Prism Tapertope Bicupolic_ring]]> |
| - | | | + | {{STS Shape |
| + | | image=<[#embed [hash 2Y6EC6FJBFXCPWWPHGZ9G626QE] [width 120]]> | ||
| name=Tetrahedral prism | | name=Tetrahedral prism | ||
| dim=4 | | dim=4 | ||
| elements=6, 15, 16, 8 | | elements=6, 15, 16, 8 | ||
| genus=1 | | genus=1 | ||
| - | |||
| ssc=[xG3P] | | 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> | | vlayout=([[Triangle|3]][[Tetrahedron|<sup>3</sup>]])⋅([[Triangle|3]]⋅[[Square|4]]<sup>2</sup>)<sup>3</sup> | ||
| vfigure=[[Tetrahedron]] | | 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}} | ||
| + | {{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. 112 Tetrahedral prism | 27. [111]1 Triangular prismic pyramid |
| List of tapertopes | ||
