Gyroelongated triangular bicupola

In geometry, the gyroelongated triangular bicupola is one of the Johnson solids (Template:Math). As the name suggests, it can be constructed by gyroelongating a triangular bicupola (either triangular orthobicupola, Template:Math, or the cuboctahedron) by inserting a hexagonal antiprism between its congruent halves.

The gyroelongated triangular bicupola is one of five Johnson solids which are chiral, meaning that they have a "left-handed" and a "right-handed" form. In the illustration to the right, each square face on the bottom half of the figure is connected by a path of two triangular faces to a square face above it and to the right. In the figure of opposite chirality (the mirror image of the illustrated figure), each bottom square would be connected to a square face above it and to the left. The two chiral forms of Template:Math are not considered different Johnson solids.

Formulae

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

$V=\sqrt{2}(\frac{5}{3}+\sqrt{1+\sqrt{3}})a^3\approx 4.69456...a^3$

$A=(6+5\sqrt{3})a^2\approx 14.6603...a^2$

External links

• Template:Mathworld2