Pyritosnub tesseract

From Polytope Wiki
Jump to navigation Jump to search
Pyritosnub tesseract
Pyritosnub tesseract.gif
Bowers style acronymPysnet
Coxeter diagramx4s3s3s (CDel node 1.pngCDel 4.pngCDel node h.pngCDel 3.pngCDel node h.pngCDel 3.pngCDel node h.png)
Cells96 skewed wedges, 32 triangular prisms, 24 rectangular trapezoprisms, 16 snub tetrahedra, 8 pyritosnub cubes
Faces192 scalene triangles, 64+64 triangles, 96+96 isosceles trapezoids, 48+96 rectangles
Vertex figurePolyhedron with 1 pentagon, 1 tetragon, and 5 triangles
Measures (as derived from unit-edge great disprismatotesseractihexadecachoron)
Edge lengthsRemaining edges from class being alternated (96): 1
 Edges from diagonals of original squares (96):
 Edges of equilateral triangles (192+192):
 Long edges of rectangles (96):
Central density1
Related polytopes
DualHeptahedral hecatonenneacontadichoron
Abstract & topological properties
Euler characteristic0
SymmetryB4/2, order 192

The pyritosnub tesseract or pysnet, also known as the edge-snub hexadecachoron, is a convex isogonal polychoron that consists of 8 pyritosnub cubes, 16 snub tetrahedra, 24 rectangular trapezoprisms, 32 triangular prisms, and 96 skewed wedges. 3 wedges and one of each of the other 4 types of cells join at each vertex. It can be obtained through the process of alternating one set of 192 edges of the great disprismatotesseractihexadecachoron in such a way that the octagonal faces turn into rectangles. However, it cannot be made uniform, as it generally has 5 different edge lengths, which can be minimized to no more than 2 different sizes.

A variant with 8 regular icosahedra and 32 uniform triangular prisms can be vertex-inscribed into a prismatorhombisnub icositetrachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:a ≈ 1:1.49032, where a is the second largest real root of 37x6-50x5-81x4+40x3+80x2+32x+4.

Vertex coordinates[edit | edit source]

Vertex coordinates for a pyritosnub tesseract, created from the vertices of a great disprismatotesseractihexadecachoron of edge length 1, are given by all even permutations of:

A variant using regular icosahedra and uniform triangular prisms of edge length 1, centered at the origin, has vertices given by all even permutations of:

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by all even permutations of:


External links[edit | edit source]