Tetrahedral prism (EntityTopic, 21)

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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

@@ Line 1: / Line 1: @@
-{{Shape|Tetrahedral prism|''No image''|4|6, 14, 16, 8|1|N/A|N/A|[[Line segment|E]][[Triangle|T]][[Tetrahedron|T]]E|1<sup>2</sup>1 x<sup>yz</sup>w|[[Tetrahedron]]|Tepe|''Unknown''|26|N/A|N/A|pure|''Unknown''|''Unknown''|([[Triangle|3]][[Tetrahedron|<sup>3</sup>]])⋅([[Triangle|3]]⋅[[Square|4]]<sup>[[Triangular prism|2]]</sup>)<sup>3</sup>}}
+<[#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.
-The '''tetrahedral prism''' is a special case of a [[prism]] where the base is a [[tetrahedron]].
+== 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}}
-{{Rotope Nav|25|26|27|(I'II)<br>Triangular prismidal torus|I<nowiki>''</nowiki>I<br>Tetrahedral prism|I<nowiki>'''</nowiki><br>Pentachoron|chora}}
+{{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}}