Triangular triswirlprism
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Triangular triswirlprism | |
---|---|
File:Triangular triswirlprism.png | |
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 54 phyllic disphenoids, 18 triangular gyroprisms |
Faces | 108 scalene triangles, 54 isosceles triangles, 18 triangles |
Edges | 27+54+54 |
Vertices | 27 |
Vertex figure | 10-vertex polyhedron with 4 tetragons and 8 triangles |
Measures (based on triangular duoprisms of edge length 1) | |
Edge lengths | Short side edges (27): |
Long side edges (54): | |
Edges of triangles (54): 1 | |
Circumradius | |
Central density | 1 |
Related polytopes | |
Dual | Triangular triswirltegum |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | (I2(9)≀S2)+/3, order 108 |
Convex | Yes |
Nature | Tame |
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).