Gyroelongated triangular bicupola

In geometry, the gyroelongated triangular bicupola is one of the Johnson solids ($J43 – J44 – J45$). As the name suggests, it can be constructed by gyroelongating a triangular bicupola (either triangular orthobicupola, $D3$, 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 $6(3.4.3.4) 2.6(34.4)$ 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:


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


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