Cubic truncate (EntityTopic, 11)

From Hi.gher. Space

(Difference between revisions)
m (add symmetry group)
 
(13 intermediate revisions not shown)
Line 1: Line 1:
 +
<[#ontology [kind topic] [cats 3D Uniform Polytope]]>
{{STS Shape
{{STS Shape
-
| image=http://teamikaria.com/share/?caption=Truncatedcube.png
+
| image=<[#embed [hash QYFV033ABJAQM48N5ATZJJTT0Y] [width 180]]>
| dim=3
| dim=3
| elements=14, 36, 24
| elements=14, 36, 24
 +
| sym=[[Staurohedral symmetry|O<sub>h</sub>, BC<sub>3</sub>, [4,3], (*432)]]
| genus=0
| genus=0
| ssc=[xyz]X3
| ssc=[xyz]X3
-
| extra={{STS Uniform polytope
+
| 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]]}
| schlaefli=t{[[Square|4,]][[Cube|3]]}
 +
| conway=t[[Cube|d]][[Octahedron|a]][[Tetrahedron|Y3]]
| vfigure=Isosceles [[triangle]]
| vfigure=Isosceles [[triangle]]
| vlayout=[[Triangle|3]]∙[[Octahedron|8]]<sup>2</sup>
| vlayout=[[Triangle|3]]∙[[Octahedron|8]]<sup>2</sup>
-
| bowers=Tic
 
-
| kana=キュト
 
-
| dual=[[Triakis octahedron]]
 
}}}}
}}}}
 +
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}}

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

#TXIDVaEaEb8a3aTypeName
0 Va = point ;
1 Ea 2 = digon ;
2 Eb 2 = digon ;
3 8a 844 = octagon ;
4 3a 303 = triangle ;
5 C1a 24122468 = truncated cube ;

Usage as facets

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


Notable Trishapes
Regular: tetrahedroncubeoctahedrondodecahedronicosahedron
Direct truncates: tetrahedral truncatecubic truncateoctahedral truncatedodecahedral truncateicosahedral truncate
Mesotruncates: stauromesohedronstauroperihedronstauropantohedronrhodomesohedronrhodoperihedronrhodopantohedron
Snubs: snub staurohedronsnub rhodohedron
Curved: spheretoruscylinderconefrustumcrind