Joined hexadecachoron

The joined tesseract, joined square duoprism, or transitional digonal double tegmotrapezohedroid, also known as the triangualr -bipyramidal triacontadichoron or tibbit, is a convex isochoric polychoron with 32 triangular bipyramids as cells. It can be obtained as the dual of the rectified tesseract.

As the joined square duotegum, it is the square member of an infinite family of isogonal joined duotegums.

It can also be obtained as the convex hull of a tesseract and a hexadecachoron, where the edges of the tesseract are $$\frac{3\sqrt2}{2}$$ times the length of those of the hexadecachoron.

The ratio between the longest and shortest edges is 1:$$\frac{3\sqrt{14}}{7}$$ ≈ 1:1.60357. Each face is an isosceles triangle that uses one long and two short edges.

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Triangular bipyramid (32): Rectified icositetrachoron
 * Isosceles triangle (96): Semi-uniform small rhombated tesseract
 * Edge (24): Icositetrachoron
 * Edge (64): Semi-uniform small disprismatotesseractihexadecachoron
 * Vertex (8): Hexadecachoron
 * Vertex (16): Tesseract