Pyritosnub penteract

Pyritosnub penteract
File:Pyritosnub penteract.png (OFF file)
Rank	5
Type	Isogonal
Notation
Bowers style acronym	Pysnan
Coxeter diagram	x4s3s3s3s
Elements
Tera	960 tetrahedral wedges, 80 triangular-square prismantiprismoids, 80 snub tetrahedral prisms, 40 pyritosnub alterprisms, 32 snub pentachora, 10 pyritosnub tesseracts
Cells	1920 irregular tetrahedra, 960+960+960+960 wedges, 320+320 triangular prisms, 320+320 triangular gyroprisms, 160+240+240 rectangular trapezoprisms, 160+160 snub tetrahedra, 80 pyritosnub cubes
Faces	1920+1920+1920+1920 scalene triangles, 640+640+640 triangles, 960+960+960 isosceles trapezoids, 480+480+960+960 rectangles
Edges	960+960+960+960+960+1920+1920+1920
Vertices	1920
Measures (based on great cellipenteractitriacontaditeron of edge length 1
Edge lengths	Remaining original edges (960): 1
	Diagonals of squares (960+960+960): ${\sqrt {2}}\approx 1.41421$
	Edges of equilateral triangles (1920+1920+1920): ${\sqrt {3}}\approx 1.73205$
	Long edges of rectangles (960): $1+{\sqrt {2}}\approx 2.41421$
Central density	1
Related polytopes
Dual	Hendecachoric chilliaenneacosiicosateron
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B5/2, order 1920
Convex	Yes
Nature	Tame

The pyritosnub penteract or pysnan, also known as the edge-snub triacontaditeron, is a convex isogonal polyteron that consists of 10 pyritosnub tesseracts, 32 snub pentachora, 40 pyritosnub alterprisms, 80 snub tetrahedral prisms, 80 triangular-square prismantiprismoids, and 960 tetrahedral wedges. 4 tetrahedral wedges and 1 of each of the other facet types join at each vertex. It can be obtained through the process of obtained through the process of edge-alternating the great cellipenteractitriacontaditeron so that the octagons become long rectangles. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\frac {3+2{\sqrt {6}}}{5}}$ ≈ 1:1.57980.

Vertex coordinates

The vertices of a pyritosnub penteract, assuming that the edge length differences are minimized via the ratio method, centered at the origin, are given by all even permutations and all sign changes of:

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

External links

• Klitzing, Richard. "pysnan".