Castellated rhodoperihedral prism (EntityTopic, 15)
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<blockquote>total edge length = 492''l''<br /> | <blockquote>total edge length = 492''l''<br /> | ||
total surface area = (60 + 70√3 + 21√(25+10√5)) {{DotHV}}<br /> | total surface area = (60 + 70√3 + 21√(25+10√5)) {{DotHV}}<br /> | ||
| - | surcell volume = | + | surcell volume = {{Over|1|3}} · (60φ<sup>2</sup> + 197φ + 74 + 10√2) {{DotHV|3}}<br /> |
bulk = ''Unknown''</blockquote> | bulk = ''Unknown''</blockquote> | ||
{{Trishapes}} | {{Trishapes}} | ||
Revision as of 23:37, 5 February 2014
The castellated rhodoperihedral prism is a crown jewel CRF polychoron discovered on February 4, 2014 by quickfur and confirmed by Klitzing.[1] Although it is not strictly a prism (as it's not the Cartesian product of a base shape with a digon) it is so named as it has similar structure to "real" prisms of uniform polyhedra.
Its cells are two rhodoperihedra, 24 pentagonal pyramids, 40 tetrahedra and 30 bilunabirotundae (bilbiro). The rhodoperihedra form the "ends" of the prism, and are orthogonal to the bilbiro, which form the "sides" of the prism.
Its faces are 40 "end" triangles (x3o), 60 "end" squares (x2x), 24 "end" pentagons (o5x), 120 "lune-facing side" triangles (xo&#x), 120 "rotunda-facing side" triangles (xo&#x) and 60 "side" pentagons (ooooo3ooooo5ooooo&#xt).
It has 120 + 120 + 120 + 120 + 12 = 492 edges and 120 + 24 + 20 = 164 vertices.
Equations
- The hypervolumes of a castellated rhodoperihedral prism with side length l are given by:
total edge length = 492l
total surface area = (60 + 70√3 + 21√(25+10√5)) · l2
surcell volume = 1∕3 · (60φ2 + 197φ + 74 + 10√2) · l3
bulk = Unknown
| 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 |
