Rank4
TypeUniform
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${\displaystyle {\sqrt {\frac {3+{\sqrt {2}}}{2}}}\approx 1.48563}$
Hypervolume${\displaystyle {\frac {19+8{\sqrt {2}}}{6}}\approx 5.05228}$
Dichoral anglesTet–3–trip: 150°
Cube–4–trip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
Cube–4–op: 90°
Op–8–op: 90°
Trip–4–op: ${\displaystyle \arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }}$
Central density1
Number of external pieces80
Level of complexity30
Related polytopes
ArmySidpith
RegimentSidpith
Convex coreTesseract
Abstract & topological properties
Flag count3072
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.

Jonathan Bowers wrote that the acronym iquipadah occurred to him in church before actually discovering the figure.[1]

## Vertex coordinates

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