Castellated rhodoperihedral prism (EntityTopic, 15)
From Hi.gher. Space
(it was actually discovered on the evening the day before (check the date of my first post :P)) |
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| - | The '''castellated rhodoperihedral prism''' is a [[crown jewel]] [[CRF polychoron]] discovered on | + | The '''castellated rhodoperihedral prism''' is a [[crown jewel]] [[CRF polychoron]] discovered on February 4, 2014 by [[quickfur]] and confirmed by [[Klitzing]].[http://teamikaria.com/hddb/forum/viewtopic.php?p=20029#p20029] 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 pyramid]]s, 40 [[tetrahedra]] and 30 [[bilunabirotunda]]e (bilbiro). The rhodoperihedra form the "ends" of the prism, and are orthogonal to the bilbiro, which form the "sides" of the prism. | Its cells are two [[rhodoperihedra]], 24 [[pentagonal pyramid]]s, 40 [[tetrahedra]] and 30 [[bilunabirotunda]]e (bilbiro). The rhodoperihedra form the "ends" of the prism, and are orthogonal to the bilbiro, which form the "sides" of the prism. | ||
Revision as of 07:55, 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 = Unknown
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 |
