Gyroelongated triangular bicupola

Template:Short description {{#invoke:Infobox|infobox}}Template:Template other

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:<ref>Stephen Wolfram, "Gyroelongated triangular bicupola" from Wolfram Alpha. Retrieved July 30, 2010.</ref>

<math>V= \sqrt{2} \left(\frac{5}{3}+\sqrt{1+\sqrt{3}}\right) a^3 \approx 4.69456...a^3</math>

<math>A=\left(6+5\sqrt{3}\right)a^2 \approx 14.6603...a^2</math>

External links

• Template:Mathworld2