Dodecahedral cupola
In 4-dimensional geometry, the dodecagonal cupola is a polychoron bounded by a rhombicosidodecahedron, a parallel dodecahedron, connected by 30 triangular prisms, 12 pentagonal prisms, and 20 tetrahedra.[1]
| Dodecahedral cupola | ||
|---|---|---|
 Schlegel diagram | ||
| Type | Polyhedral cupola | |
| Schläfli symbol | {5,3} v rr{5,3} | |
| Cells | 64 | 1 rr{5,3}  1 {5,3}  30 {}×{3}  12 {}×{5}  20 {3,3}  |
| Faces | 194 | 80 triangles 90 squares 24 pentagons |
| Edges | 210 | |
| Vertices | 80 | |
| Dual | ||
| Symmetry group | [5,3,1], order 120 | |
| Properties | convex, regular-faced | |
Related polytopes
The dodecahedral cupola can be sliced off from a runcinated 120-cell, on a hyperplane parallel to a dodecahedral cell. The cupola can be seen in a pentagonal centered orthogonal projection of the runcinated 120-cell:
Runcinated 120-cell |
Dodecahedron (cupola top) |
Rhombicosidodecahedron (cupola base) |
gollark: > 10 percent of BLM protests are violent. that means if you have 12 protests in your area you are guaranteed to be hurt, or have property damageRandom nitpicking, but that is *not* how probabilities work.
gollark: Although, I'm not sure how a "no capital system" is meant to work, given that you need capital to produce basically anything.
gollark: Lots of the things fitting into each category are completely different from each other in other ways.
gollark: But that's not necessarily a *good* dichotomy.
gollark: Well, if you split the entire possible space of economic systems into two areas, then yes, things go into those two areas.
See also
References
- Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.152 dodecahedron || rhombicosidodecahedron)
External links
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