Joined icositetrachoron

The joined icositetrachoron, also known as the triangular-bipyramidal enneacontahexachoron or tabene,' is a convex isochoric polychoron with 96 triangular bipyramids as cells. It can be obtained as the dual of the rectified icositetrachoron.

It can also be obtained as the convex hull of 2 dually-oriented icositetrachora, where one has edge length $$\frac{3\sqrt2}{4}$$ times that of the other.

The ratio between the longest and shortest edges is 1:$$\frac{3\sqrt5}{5}$$ ≈ 1:1.34164. Each face is an isosceles triangle that uses one long and two short edges.

Variations
The joined icositetrachoron has variants that remain isochoric under BC4 symmetry (called the great notched enneacontahexachoron) and D4 symmetry (called the skewed notched enneacontahexachoron).

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Triangular bipyramid (96): Rectified icositetrachoron
 * Isosceles triangle (288): Small rhombated icositetrachoron
 * Edge (96): Rectified icositetrachoron
 * Edge (144): Semi-uniform small prismatotetracontoctachoron
 * Vertex (24): Icositetrachoron
 * Vertex (24): Icositetrachoron