 Rank4
TypeUniform
SpaceSpherical
Notation
Elements
Cells16 tetrahedra, 32 triangular prisms, 16 cubes, 8 octagonal prisms
Faces64 triangles, 32+32+64 squares, 8 octagons
Edges32+32+64+64
Vertices64
Vertex figureBlend of triangular antipodium and digonal disphenoid
Measures (edge length 1)
Circumradius$\sqrt{\frac{3+\sqrt2}{2}} ≈ 1.48563$ Hypervolume$\frac{19+8\sqrt{2}}{6} ≈ 5.05228$ Dichoral anglesTet–3–trip: 150°
Cube–4–trip: $\arccos\left(-\frac{\sqrt6}{3}\right) ≈ 144.73561°$ Cube–4–op: 90°
Op–8–op: 90°
Trip–4–op: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561°$ Central density1
Number of external pieces80
Level of complexity30
Related polytopes
ArmySidpith
RegimentSidpith
Convex coreTesseract
Abstract & topological properties
Euler characteristic–8
OrientableYes
Properties
SymmetryB2≀S2, order 128
ConvexNo
NatureWild

The inverted quasiprismatodishexadecachoron, or iquipadah, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra, 32 triangular prisms, 16 cubes, and 8 octagonal prisms. 1 tetrahedron, 3 triangular prisms, 2 cubes, and 2 octagonal prisms meet at each vertex.

It can be created by blending a small disprismatotesseractihexadecachoron with an octagonal diorthoprism, an inscribed compound of 2 square-octagonal duoprisms. In the process 16 cubical cells blend out.

Its vertex figure is concave, a property shared by sanbathi.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small disprismatotesseractihexadecachoron.