Square triswirlprism

Square triswirlprism
File:Square triswirlprism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	96 phyllic disphenoids, 24 square gyroprisms
Faces	192 scalene triangles, 96 isosceles triangles, 24 squares
Edges	48+96+96
Vertices	48
Vertex figure	10-vertex polyhedron with 4 tetragons and 8 triangles
Measures (based on square duoprisms of edge length 1)
Edge lengths	Short side edges (48): $\frac{\sqrt6-\sqrt2}{2} ≈ 0.51764$
	Long side edges (96): $\sqrt{\frac{3-\sqrt3}{2}} ≈ 0.79623$
	Edges of squares (96): 1
Circumradius	1
Central density	1
Related polytopes
Dual	Square triswirltegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	(I2(12)≀S2)+/3, order 192
Convex	Yes
Nature	Tame

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:$\sqrt{2+\sqrt3}$ ≈ 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).