Cubic pyramid (EntityTopic, 23)
From Hi.gher. Space
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| name=Cubic pyramid | | name=Cubic pyramid | ||
| dim=4 | | dim=4 | ||
| + | | image=<[#embed [hash YBP0RT0PWBX7TAFHCF3JWCMKHH] [width 180]]> | ||
| elements=7, 18, 20, 9 | | elements=7, 18, 20, 9 | ||
| genus=0 | | genus=0 | ||
Revision as of 19:25, 27 March 2014
Equations
- Variables:
l ⇒ length of edges of the cubic pyramid
- The hypervolumes of a cubic pyramid are given by:
total edge length = 20l
total surface area = (6 + 3√3) · l2
surcell volume = (1 + √2) · l3
bulk = 1∕4 · l4
- The realmic cross-sections (n) of a cubic pyramid are:
[!x,!y,!z] ⇒ triangle
[!w] ⇒ square
Net
The net of a cubic pyramid is a cube surrounded by six square pyramids.
Incidence matrix
Dual: octahedral pyramid
| # | TXID | Va | Vb | Ea | Eb | 3a | 4a | C1a | C2a | Type | Name |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; sweep: apex | ||||||||
| 1 | Vb | = point | ; lateral: vertices | ||||||||
| 2 | Ea | 1 | 1 | = digon | ; sweep: vertices | ||||||
| 3 | Eb | 0 | 2 | = digon | ; lateral: edges | ||||||
| 4 | 3a | 1 | 2 | 2 | 1 | = triangle | ; sweep: edges | ||||
| 5 | 4a | 0 | 4 | 0 | 4 | = square | ; lateral: faces | ||||
| 6 | C1a | 1 | 4 | 4 | 4 | 4 | 1 | = square pyramid | ; sweep: faces | ||
| 7 | C2a | 0 | 8 | 0 | 12 | 0 | 6 | = base of pyramid: cube | ; lateral: cell | ||
| 8 | H4.1a | 1 | 8 | 8 | 12 | 12 | 6 | 6 | 1 | = cubic pyramid | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
| Notable Tetrashapes | |
| Regular: | pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron |
| Powertopes: | triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate |
| Circular: | glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder |
| Torii: | tiger • torisphere • spheritorus • torinder • ditorus |
| 18. [21]1 Cylindrone | 19. [111]1 Cubic pyramid | 20. 211 Cyltrianglinder |
| List of tapertopes | ||
