# Square triswirlprism

Square triswirlprism
File:Square triswirlprism.png
Rank4
TypeIsogonal
Elements
Cells96 phyllic disphenoids, 24 square gyroprisms
Faces192 scalene triangles, 96 isosceles triangles, 24 squares
Edges48+96+96
Vertices48
Vertex figure10-vertex polyhedron with 4 tetragons and 8 triangles
Measures (based on square duoprisms of edge length 1)
Edge lengthsShort side edges (48): ${\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{2}}\approx 0.51764}$
Long side edges (96): ${\displaystyle {\sqrt {\frac {3-{\sqrt {3}}}{2}}}\approx 0.79623}$
Edges of squares (96): 1
Central density1
Related polytopes
DualSquare triswirltegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(12)≀S2)+/3, order 192
ConvexYes
NatureTame

The square triswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 24 square gyroprisms and 96 phyllic disphenoids. 4 square gyroprisms and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the dodecagonal duoprism. It is the third in an infinite family of isogonal square dihedral swirlchora.

The ratio between the longest and shortest edges is 1:${\displaystyle {\sqrt {2+{\sqrt {3}}}}}$ ≈ 1:1.93185.

## Vertex coordinates

Coordinates for the vertices of a square triswirlprism constructed as the convex hull of three square duoprisms of edge length 1, are given as Cartesian products of the vertices of square S1:

• S1 × S1,
• S2 × S2 (S1 rotated 30 degrees),
• S3 × S3 (S1 rotated 60 degrees).