# Sphenocorona

Sphenocorona
TypeJohnson
J85 - J86 - J87
Faces2x2+2x4 triangles
2 squares
Edges22
Vertices10
Vertex configuration4(33.4)
2(32.42)
2x2(35)
Symmetry groupC2v
Dual polyhedron-
Propertiesconvex
Net

In geometry, the sphenocorona is one of the Johnson solids (J86).

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.[1]

The sphenocorona is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids.

## Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[2]

${\displaystyle V=\left({\frac {1}{2}}{\sqrt {1+3{\sqrt {\frac {3}{2}}}+{\sqrt {13+3{\sqrt {6}}}}}}\right)a^{3}\approx 1.51535...a^{3}}$

${\displaystyle A=\left(2+3{\sqrt {3}}\right)a^{2}\approx 7.19615...a^{2}}$