Pentagonal pyramid (EntityTopic, 12)
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A pentagonal pyramid is a special case of a pyramid where the base is a pentagon.
Equations
- The hypervolumes of a pentagonal pyramid with side length l are given by:
total edge length = 10l
surface area = 1∕4 · (5√3 + √(25+10√5)) · l2
volume = 1∕24 · (5 + √5) · l3
Incidence matrix
Dual: Self-dual
# | TXID | Va | Vb | Ea | Eb | 3a | 5a | Type | Name |
---|---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; | ||||||
1 | Vb | = point | ; | ||||||
2 | Ea | 1 | 1 | = digon | ; | ||||
3 | Eb | 0 | 2 | = digon | ; | ||||
4 | 3a | 1 | 2 | 2 | 1 | = triangle | ; | ||
5 | 5a | 0 | 5 | 0 | 5 | = base of pyramid: pentagon | ; | ||
6 | C1a | 1 | 5 | 5 | 5 | 5 | 1 | = pentagonal pyramid | ; |
Usage as facets
- 24× 1-facets of a castellated rhodoperihedral prism
- 24× 1-facets of a D4.3.1 dual
- 4× 1-facets of a bilunabirotunda pseudopyramid
- 3× 1-facets of a triangular hebesphenorotunda pseudopyramid (named pen to roof)
- 24× 1-facets of a triangular hebesphenorotundaeic rhombochoron
- 24× 1-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron (named oggbbp)
- 12× 1-facets of a D4.7
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 |