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| + | {{Infobox shape|title3 = Medial omnicircumfacetopental triakishecatonicosachoron |
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| + | |image1 = Mom fapp.png |
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| + | |dimensionality = 4 |
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| + | |bowers_acronym = '''mom fapathi''' |
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| − | 120 [[small icosicosidodecahedron|small icosicosidodecahedra]]|tera = 1 medial omnicircumfacetopental triakishecatonicosachoron|image1 = Mom fapp.png|bowers_acronym = '''mom fapathi'''|title3 = Medial omnicircumfacetopental triakishecatonicosachoron|vertices = 720 [[point]]s|edges = 3600 [[line segment]]s|faces = 1440 [[pentagram]]s |
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| + | |euler_characteritic = 2520 |
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| + | |vertices = 720 [[point]]s |
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| + | |edges = 3600 [[line segment]]s |
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| + | |faces = 1440 [[pentagram]]s |
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2400 [[triangle]]s |
2400 [[triangle]]s |
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1200 [[hexagon]]s |
1200 [[hexagon]]s |
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| + | 120 [[small icosicosidodecahedron|small icosicosidodecahedra]] |
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| + | |tera = 1 medial omnicircumfacetopental triakishecatonicosachoron |
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|vertex_count = <math>720</math> |
|vertex_count = <math>720</math> |
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|edges_length = <math>3600l</math> |
|edges_length = <math>3600l</math> |
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| − | }}A '''medial omnicircumfacetopental triakishecatonicosachoron''', better known by its rather humourous Bowers acronym "'''mom fapathi'''"<sup><ref>http://www.polytope.net/hedrondude/rox.htm</ref></sup> or "'''mommy'''" is a [[List of Uniform Polychora|uniform polychoron]] in the [[rectified great hecatonicosachoron]] regiment with 720 vertices, 3600 edges, 5760 faces, and 360 [[cell]]s. |
+ | }}A '''medial omnicircumfacetopental triakishecatonicosachoron''', better known by its rather humourous Bowers acronym "'''mom fapathi'''"<sup><ref>http://www.polytope.net/hedrondude/rox.htm</ref></sup> or as "'''mommy'''" is a [[List of Uniform Polychora|uniform polychoron]] in the [[rectified great hecatonicosachoron]] regiment with 720 vertices, 3600 edges, 5760 faces, and 360 [[cell]]s. |
==Structure and Sections== |
==Structure and Sections== |
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| − | + | [[File:MOMFPTHI.jpg|thumb]] |
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| + | The mom fapathi is in the same army as the [[rectified hexacosichoron]] ('''rox'''). This means that it shares the same vertex arrangement and vertex count as rox. Although it shares the same vertices as rox, the arrangement for higher subfacets of mom fapathi is different. The mom fapathi is in the rectified great hecatonicosachoron ('''righi''') regiment. This means that it has the same edge arrangement and edge count as righi. Being in the same regiment as righi also implies that the relationship between the circumradius and edge length of a mom fapathi is the same as righi's, which is <math>l\sqrt{\frac{5+\sqrt{5}}{2}}</math> for edge length <math>l</math>. |
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| + | The [[vertex figure]] of a mom fapathi is a '''long omnicircumfaceted pentagonal prism'''. The shape is a self-intersecting polyhedron and variant of a faceted pentagonal prism whose height is longer than the individual edge length of the pentagon. |
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=== Hypervolumes === |
=== Hypervolumes === |
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*[[vertex count]] = <math>720</math> |
*[[vertex count]] = <math>720</math> |
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Revision as of 22:24, 5 December 2019
A medial omnicircumfacetopental triakishecatonicosachoron, better known by its rather humourous Bowers acronym "mom fapathi"[1] or as "mommy" is a uniform polychoron in the rectified great hecatonicosachoron regiment with 720 vertices, 3600 edges, 5760 faces, and 360 cells.
Structure and Sections
The mom fapathi is in the same army as the rectified hexacosichoron (rox). This means that it shares the same vertex arrangement and vertex count as rox. Although it shares the same vertices as rox, the arrangement for higher subfacets of mom fapathi is different. The mom fapathi is in the rectified great hecatonicosachoron (righi) regiment. This means that it has the same edge arrangement and edge count as righi. Being in the same regiment as righi also implies that the relationship between the circumradius and edge length of a mom fapathi is the same as righi's, which is for edge length .
The vertex figure of a mom fapathi is a long omnicircumfaceted pentagonal prism. The shape is a self-intersecting polyhedron and variant of a faceted pentagonal prism whose height is longer than the individual edge length of the pentagon.
Hypervolumes
Subfacets
- 720 points (0D)
- 3600 line segments (1D)
- 1440 pentagrams (2D)
- 2400 triangles (2D)
- 720 pentagons (2D)
- 1200 hexagons (2D)
- 120 small stellated dodecahedra (3D)
- 120 icosidodecahedra (3D)
- 120 small icosicosidodecahedra (3D)
- 1 medial omnicircumfacetopental triakishecatonicosachoron (4D)
See Also
| Pentagonal rectates |
|---|
| Rectified hexacosachoron regiment: rox · rofix · sophi · sprapivady · frox · rixhi · sriphi · ipixady · lifpipixhi · nipixady · som fapathi · sofapathi · smiffipathi · paphiny · sirphinady
Rectified great hecatonicosachoron regiment: righi · raghi · papvixhi · giprapivady · froghi · ridhei · mriphi · sipathi · lifpixady · snipathi · mom fapathi · gofapathi · mim fipathi · pixhiny · girphinady Rectified great stellated hecatonicosachoron regiment: ragishi · ragashi · spapivady · prap vixhi ·frogshi · rihix ·griphi · mipathi · sliffipathi · minnipathi · gom fapathi · ofapaxady · gam fipathi · spidhiny · irp xanady Rectified great faceted hexacosichoron regiment: rigfix · raggix · gippapivady · quiphi · frogfix · ripahi · graphi · gipathi · gliffipathi · ganipathi · omfapaxady · ofpipixhi · mif pixady · gipdohiny · irp panady |