Triangular triswirltegum

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Triangular triswirltegum
Rank4
TypeIsotopic
Elements
Cells27 12-vertex decahedra
Faces54 isosceles triangles, 54 rhombi, 27 rectangular-symmetric hexagons
Edges18+54+108
Vertices18+54
Vertex figure54 phyllic disphenoids, 18 triangular gyrotegums
Measures (edge length 1)
Central density1
Related polytopes
DualTriangular triswirlprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(9)≀S2)+/3, order 108
ConvexYes
NatureTame

The triangular triswirltegum is a convex isochoric polychoron and member of the duoprismatic swirltegum family with 27 identical cells. It is the third in an infinite family of isochoric triangular hosohedral swirlchora.

Each cell of this polychoron has chiral digonal prismatic symmetry, with 2 rectangular-symmetric hexagons, 4 rhombi, and 4 isosceles triangles for faces.