Pentagonal cupola

Pentagonal cupola
Type	Johnson J4 - J5 - J6
Faces	5 triangles 5 squares 1 pentagon 1 decagon
Edges	25
Vertices	15
Vertex configuration	10(3.4.10) 5(3.4.5.4)
Symmetry group	C5v, [5], (*55)
Rotation group	C5, [5]+, (55)
Dual polyhedron	-
Properties	convex
Net

In geometry, the pentagonal cupola is one of the Johnson solids (J₅). It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares, 1 pentagon, and 1 decagon.

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.

The following formulae for volume, surface area and circumradius can be used if all faces are regular, with edge length a:

${\displaystyle V=\left({\frac {1}{6}}\left(5+4{\sqrt {5}}\right)\right)a^{3}\approx 2.32405...a^{3}}$

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Wikipedia