# Pentagonal pyramid (EntityTopic, 12)

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

 # TXID Type Name Va Vb Ea Eb 3a 5a 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

 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