Difold ditetraswirlchoron

Difold ditetraswirlchoron
	(OFF file)
Rank	4
Type	Isogonal
Elements
Cells	24 phyllic disphenoids, 16 triangular pyramids, 8 triangular gyroprisms
Faces	48 scalene triangles, 48 isosceles triangles, 16 triangles
Edges	8+24+48
Vertices	16
Vertex figure	10-vertex polyhedron with 3 tetragons and 10 triangles
Measures (circumradius 1, based on a 2D regular dodecagonal envelope)
Edge lengths	6-valence (8):
	6-valence (24):
	3-valence (48):
Central density	1
Related polytopes
Dual	Ditetraswirlic hexadecachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A3●K2, order 48
Convex	Yes
Nature	Tame

The difold ditetraswirlchoron, also known as the rectifold tetraswirlchoron or 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 gyroprisms, 16 triangular pyramids, and 24 phyllic disphenoids. 3 triangular gyroprisms, 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: ${\sqrt {2}}$ ≈ 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:

$\pm \left(0,\,0,\,0,\,1\right),$
$\pm \left({\frac {\sqrt {6}}{3}},\,0,\,{\frac {\sqrt {3}}{3}},\,0\right),$
$\pm \left({\frac {\sqrt {6}}{6}},\,\pm {\frac {\sqrt {2}}{2}},\,-{\frac {\sqrt {3}}{3}},\,0\right),$
$\pm \left(0,\,0,\,{\frac {1}{2}},\,{\frac {\sqrt {3}}{2}}\right),$
$\pm \left(0,\,{\frac {\sqrt {6}}{3}},\,-{\frac {1}{2}},\,{\frac {\sqrt {3}}{6}}\right),$
$\pm \left(\pm {\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {6}}{3}},\,{\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}}\right).$