Joined hexadecachoron

The joined hexadecachoron, joined square duotegum, or transitional digonal double tegmotrapezohedroid, also known as the triangular-tegmatic triacontadichoron or tibbit, is a convex isochoric polychoron with 32 triangular tegums 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 isochoric joined duotegums.

It can also be obtained as the convex hull of a tesseract and a hexadecachoron, where the edges of the hexadecachoron are $$\frac{3\sqrt2}{2} ≈ 2.12132$$ times the length of those of the tesseract.

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.

Variations
The joined hexadecachoron has a variant with D4 symmetry that remains isochoric. In this variant the tegums become apiculated triangular pyramids, and the variant could be called an apiculatotripyramidal triacontadichoron.

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Triangular tegum (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