Triangular dome

The triangular dome is a special dome with an equilateral hexagon as the base and an equilateral triangle as the top surface. The sides of the dome are bordered by three squares and three equilateral triangles, which are arranged alternately.

It is the Johnson body J ₃ of 92, all named after the mathematician Norman Johnson .

By combining two triangular domes (base on base) a cuboctahedron or an anti- cuboctahedron is created .

Formulas

Sizes of a triangular dome with edge length a
volume	${\ displaystyle V = {\ frac {5} {6}} \, a ^ {3} {\ sqrt {2}}}$
Surface area	${\ displaystyle A_ {O} = {\ frac {a ^ {2}} {2}} \ left (6 + 5 {\ sqrt {3}} \ right)}$
Umkugelradius	${\ displaystyle R = a}$
Edge ball radius	${\ displaystyle r = {\ frac {a} {2}} {\ sqrt {3}}}$

Web links

Eric W. Weisstein : triangular dome . In: MathWorld (English).
Eric W. Weisstein : The Johnson Bodies . In: MathWorld (English).