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 duoprism, it is the square member of an infinite family of isogonal joined duoprisms.

It can also be obtained as the convex hull of a tesseract and a hexadecachoron, where the edges of the hexadecachoron are $$\frac{3\sqrt2}{2}$$ 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 tesseract has a variant with D4 symmetry that remains isogonal. In this variant the bipyramids 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 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