Triangular triswirlprism

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Triangular triswirlprism
File:Triangular triswirlprism.png
Rank4
TypeIsogonal
Elements
Cells54 phyllic disphenoids, 18 triangular gyroprisms
Faces108 scalene triangles, 54 isosceles triangles, 18 triangles
Edges27+54+54
Vertices27
Vertex figure10-vertex polyhedron with 4 tetragons and 8 triangles
Measures (based on triangular duoprisms of edge length 1)
Edge lengthsShort side edges (27):
 Long side edges (54):
 Edges of triangles (54): 1
Circumradius
Central density1
Related polytopes
DualTriangular triswirltegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(9)≀S2)+/3, order 108
ConvexYes
NatureTame

The triangular triswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 18 triangular gyroprisms and 54 phyllic disphenoids. 4 triangular gyroprisms and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the enneagonal duoprism. It is the third in an infinite family of isogonal triangular dihedral swirlchora.

The ratio between the longest and shortest edges is 1: ≈ 1:1.79046.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a triangular triswirlprism constructed as the convex hull of three triangular duoprisms of edge length 1, are given as Cartesian products of the vertices of triangle T1:

  • T1 × T1,
  • T2 × T2 (T1 rotated 40 degrees),
  • T3 × T3 (T1 rotated 80 degrees).