Cubic truncate (EntityTopic, 11)

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(Difference between revisions)

Latest revision as of 11:12, 2 March 2014

The cubic truncate (CT) is a uniform polyhedron which can be seen as a 3-dimensional analog of the octagon. The other possible analog is the cuboctahedral rectate (COR). While the CT has the octagons on the surface of the shape, the COR has them embedded inside it. Thus when one is concerned with powertopes, the COR comprises three "long and thin" cuboids whereas the CT comprises three "wide and flat" cuboids.

Incidence matrix

Dual: triakis octahedron

#	TXID	Va	Ea	Eb	8a	3a	Type	Name
0	Va						= point	;
1	Ea	2					= digon	;
2	Eb	2					= digon	;
3	8a	8	4	4			= octagon	;
4	3a	3	0	3			= triangle	;
5	C1a	24	12	24	6	8	= truncated cube	;

Usage as facets

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

Notable Trishapes
Regular:	tetrahedron • cube • octahedron • dodecahedron • icosahedron
Direct truncates:	tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate
Mesotruncates:	stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron
Snubs:	snub staurohedron • snub rhodohedron
Curved:	sphere • torus • cylinder • cone • frustum • crind

@@ Line 1: / Line 1: @@
-{{Shape|Truncated cube|http://fusion-global.org/share/Truncatedcube.png|3|14, 36, 24|0|t{[[Square|4,]][[Cube|3]]}|''Unknown''|[[Line segment|E]][[Square|E]][[Cube|E]]X<sub>2</sub>|N/A|Isosceles [[triangle]]|Tic|[[Triakis octahedron]]|N/A|N/A|N/A|none|''Unknown''|''Unknown''|[[Triangle|3]]∙[[Octahedron|8]]<sup>2</sup>}}
+<[#ontology [kind topic] [cats 3D Uniform Polytope]]>
+{{STS Shape
+| image=<[#embed [hash QYFV033ABJAQM48N5ATZJJTT0Y] [width 180]]>
+| dim=3
+| elements=14, 36, 24
+| sym=[[Staurohedral symmetry|O<sub>h</sub>, BC<sub>3</sub>, [4,3], (*432)]]
+| genus=0
+| ssc=[xyz]X3
+| ssc2=Ko3
+| extra={{STS Polytope
+| flayout={{FLD|a3|i|a4|er}}
+| dual=[[Triakis octahedron]]
+| bowers=Tic
+}}{{STS Uniform polytope
+| schlaefli=t{[[Square|4,]][[Cube|3]]}
+| conway=t[[Cube|d]][[Octahedron|a]][[Tetrahedron|Y3]]
+| vfigure=Isosceles [[triangle]]
+| vlayout=[[Triangle|3]]∙[[Octahedron|8]]<sup>2</sup>
+}}}}
+The '''cubic truncate''' ('''CT''') is a uniform polyhedron which can be seen as a 3-dimensional analog of the [[octagon]]. The other possible analog is the [[cuboctahedral rectate]] (''COR''). While the CT has the octagons on the surface of the shape, the COR has them embedded inside it. Thus when one is concerned with [[powertopes]], the COR comprises three "long and thin" cuboids whereas the CT comprises three "wide and flat" cuboids.
-{{Trishapes}}
+<[#polytope [id 10]]>
-[[Category:Uniform polyhedra]]
+{{Trishapes}}