# Square duotruncatoprism

Square duotruncatoprism Rank4
TypeIsogonal
SpaceSpherical
Notation
Bowers style acronymSquidtep
Elements
Cells16 tetragonal disphenoids, 32 wedges, 16 rectangular trapezoprisms, 8 ditetragonal prisms
Faces64 isosceles triangles, 64 isosceles trapezoids, 32+32 rectangles, 8 ditetragons
Edges32+32+64+64
Vertices64
Vertex figureMirror-symmetric bi-apiculated tetrahedron
Measures (based on octagon edge length 1 and same radius ratio as uniform-derived square duoexpandoprism)
Edge lengthsEdges of octagons (32+32): 1
Lacing edges (64): $\sqrt{2+\sqrt2} ≈ 1.84776$ Edges of pseudo-squares (64): $2+\sqrt2 ≈ 3.41421$ Circumradius$\sqrt{\frac{8+5\sqrt2}{2}} ≈ 2.74509$ Central density1
Related polytopes
ArmySquidtep
RegimentSquidtep
DualSquare duotruncatotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB2≀S2, order 128
ConvexYes
NatureTame

The square duotruncatoprism or squidtep is a convex isogonal polychoron and the third member of the duotruncatoprism family. It consists of 8 ditetragonal prisms, 16 rectangular trapezoprisms, 32 wedges, and 16 tetragonal disphenoids. 2 ditetragonal prisms, 2 rectangular trapezoprisms, 3 wedges, and 1 tetragonal disphenoid join at each vertex. It can be obtained as the convex hull of two orthogonal semi-uniform square-ditetragonal duoprisms whose ditetragonal prism cells have a smaller circumradius than their square prisms. Although it cannot be made uniform while remaining convex, it is isomorphic to the inverted quasiprismatodishexadecachoron.