Stauromesohedron (EntityTopic, 11)
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| + | <[#ontology [kind topic] [cats 3D Uniform Polytope]]> | ||
{{STS Shape | {{STS Shape | ||
| - | | image=<[# | + | | image=<[#embed [hash FKJ1YFBZ7JRGY2KGTB03GNB1KJ] [width 180]]> |
| dim=3 | | dim=3 | ||
| - | | elements= | + | | elements=6 [[square]]s, 8 [[triangle]]s, 24 [[digon]]s, 12 [[point]]s |
| + | | sym=[[Staurohedral symmetry|O<sub>h</sub>, BC<sub>3</sub>, [4,3], (*432)]] | ||
| genus=0 | | genus=0 | ||
| - | | ssc={ | + | | ssc={G4<sup>3</sup>}x2 |
| ssc2=Ko2 | | ssc2=Ko2 | ||
| extra={{STS Polytope | | extra={{STS Polytope | ||
| flayout={{FLD|a3|i|a4|cr}} | | flayout={{FLD|a3|i|a4|cr}} | ||
| + | | petrie=6,6,0 | ||
| dual=[[Rhombic dodecahedron]] | | dual=[[Rhombic dodecahedron]] | ||
| + | | bowers=Co | ||
}}{{STS Uniform polytope | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>2 | 3 4 or 3 3 | 2</nowiki> | | wythoff=<nowiki>2 | 3 4 or 3 3 | 2</nowiki> | ||
| schlaefli=r{[[Square|4]],[[Cube|3]]}, r{[[Triangle|3]],[[Octahedron|4]]} or rr{[[Triangle|3]],[[Tetrahedron|3]]} | | schlaefli=r{[[Square|4]],[[Cube|3]]}, r{[[Triangle|3]],[[Octahedron|4]]} or rr{[[Triangle|3]],[[Tetrahedron|3]]} | ||
| + | | dynkin=o4x3o, x3o3x | ||
| conway=a[[Octahedron|a]][[Tetrahedron|Y3]] | | conway=a[[Octahedron|a]][[Tetrahedron|Y3]] | ||
| vlayout={[[Triangle|3]]⋅[[Square|4]]}<sup>2</sup> | | vlayout={[[Triangle|3]]⋅[[Square|4]]}<sup>2</sup> | ||
| vfigure=[[Rectangle]], edges 1 and √2 | | vfigure=[[Rectangle]], edges 1 and √2 | ||
| - | |||
| - | |||
}}}} | }}}} | ||
| + | The '''stauromesohedron''' is also known as the '''cuboctahedron'''. Of the six uniform mesohedra, it is the only one whose [[elemental name]] is longer (by one syllable) than its widely accepted name, however it was renamed for consistency. t has 6 squares and 8 triangles as its faces, two of each kind of face join at each vertex. | ||
| - | {{ | + | ==Equations== |
| + | *The hypervolumes of a cuboctahedron are: | ||
| + | <blockquote>total edge length=24''l'' | ||
| + | surface area= (6+2√3) · ''l''<sup>2</sup> | ||
| + | volume = {{Over|5√2|3}} · ''l''<sup>3</sup> | ||
| - | [[ | + | {{Clear}} |
| + | |||
| + | <[#polytope [id 8]]> | ||
| + | |||
| + | {{Trishapes}} | ||
Latest revision as of 16:35, 26 March 2017
The stauromesohedron is also known as the cuboctahedron. Of the six uniform mesohedra, it is the only one whose elemental name is longer (by one syllable) than its widely accepted name, however it was renamed for consistency. t has 6 squares and 8 triangles as its faces, two of each kind of face join at each vertex.
Equations
- The hypervolumes of a cuboctahedron are:
total edge length=24l surface area= (6+2√3) · l2 volume = 5√2∕3 · l3Incidence matrix
Dual: rhombic dodecahedron
# TXID Va Ea 3a 4a Type Name 0 Va = point ; 1 Ea 2 = digon ; 2 3a 3 3 = triangle ; 3 4a 4 4 = square ; 4 C1a 12 24 8 6 = stauromesohedron ; Usage as facets
- 8× 1-facets of a D4.11
- 1× 1-facets of a bitrigonal diminished pyrocantichoron
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
