Pentagonal pyramid (EntityTopic, 12)

From Hi.gher. Space

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 = 14 · (5√3 + √(25+10√5)) · l2
volume = 124 · (5 + √5) · l3

Incidence matrix

Dual: Self-dual

#TXIDVaVbEaEb3a5aTypeName
0 Va = point ;
1 Vb = point ;
2 Ea 11 = digon ;
3 Eb 02 = digon ;
4 3a 1221 = triangle ;
5 5a 0505 = base of pyramid: pentagon ;
6 C1a 155551 = pentagonal pyramid ;

Usage as facets


Notable Trishapes
Regular: tetrahedroncubeoctahedrondodecahedronicosahedron
Direct truncates: tetrahedral truncatecubic truncateoctahedral truncatedodecahedral truncateicosahedral truncate
Mesotruncates: stauromesohedronstauroperihedronstauropantohedronrhodomesohedronrhodoperihedronrhodopantohedron
Snubs: snub staurohedronsnub rhodohedron
Curved: spheretoruscylinderconefrustumcrind