Gyroelongated square cupola

In geometry, the gyroelongated square cupola is one of the Johnson solids (J₂₃). As the name suggests, it can be constructed by gyroelongating a square cupola (J₄) by attaching an octagonal antiprism to its base. It can also be seen as a gyroelongated square bicupola (J₄₅) with one square bicupola removed.

An unfolded gyroelongated square cupola, faces colored by symmetry

An unfolded gyroelongated square cupola

File:J23 gyroelongated square cupola.stl Template:-

Area and volume

The surface area is

$A=(7+2\sqrt{2}+5\sqrt{3})a^2\approx \mathrm{18.4886811...}{a}^2.$

The volume is the sum of the volume of a square cupola and the volume of an octagonal prism,

$V=(1+\frac{2}{3}\sqrt{2}+\frac{2}{3}\sqrt{4+2\sqrt{2}+2\sqrt{146+103\sqrt{2}}})a^3$ $\approx \mathrm{6.2107658...}{a}^3.$

Dual polyhedron

The dual of the gyroelongated square cupola has 20 faces: 8 kites, 4 rhombi, and 8 pentagons.

Dual gyroelongated square cupola	Net of dual

External links

• Template:Mathworld2