Triangular-antitegmatic hexacontatetrachoron

The triangular-antitegmatic hexacontatetrachoron or square duoexpandotegum is a convex isochoric polychoron with 64 triangular antitegums as cells. It can be obtained as the dual of the small disprismatotesseractihexadecachoron.

It is the square member of the infinite family of isochoric duoexpandotegums.

It can also be constructed as the convex hull of a tesseract, a hexadecachoron, an icositetrachoron (as a rectified hexadecachoron), and a rectified tesseract. If the tesseract has edge length 1, the hexadecachoron has edge length $$3-\sqrt2 ≈ 1.58579$$, the icositetrachoron has edge length $$\frac{3\sqrt2-2}{2} ≈ 1.12132$$, and the rectified tesseract has edge length $$\frac{5\sqrt2-1}{7} ≈ 0.86730$$.