Difold ditetraswirlchoron

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Difold ditetraswirlchoron
200px
Rank4
TypeIsogonal
SpaceSpherical
Info
SymmetryA3+×4, order 48
Elements
Vertex figure10-vertex polyhedron with 3 tetragons and 10 triangles
Cells16 triangular pyramids, 24 phyllic disphenoids, 8 triangular antiprisms
Faces16 triangles, 48 isosceles triangles, 48 scalene triangles
Edges8+24+48
Vertices16
Measures (circumradius 1, based on a 2D regular dodecagonal envelope)
Edge lengths6-valence (8):
 6-valence (24):
 3-valence (48):
Central density1
Euler characteristic0
Related polytopes
DualDitetraswirlic hexadecachoron
Properties
ConvexYes
OrientableYes
NatureTame

The difold ditetraswirlchoron, also known as the disphenoidal-digonal scalenohedral 8-3 double step prism, is one of several isogonal polychoron, formed as a convex hull of two hexadecachora. It consists of 8 triangular antiprisms, 16 triangular pyramids, and 24 phyllic disphenoids. 3 triangular antiprisms, 4 triangular pyramids, and 6 phyllic disphenoids join at each vertex.

This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1: ≈ 1:1.41421) would yield a tesseract instead.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a difold ditetraswirlchoron based on a 2D regular dodecagonal envelope of circumradius 1, centered at the origin, are given by:

External links[edit | edit source]