Pyritosnub alterprism

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Pyritosnub alterprism
File:Pyritosnub alterprism.png
Rank4
TypeIsogonal
Notation
Bowers style acronymPysna
Coxeter diagrams2x4s3s ()
Elements
Cells24 skewed wedges, 8 triangular gyroprisms, 6 rectangular trapezoprisms, 2 pyritosnub cubes
Faces48 scalene triangles, 16 triangles, 24+24 isosceles trapezoids, 12+12 rectangles
Edges24+24+24+24+48
Vertices48
Vertex figureTetragonal antiwedge
Measures (as derived from unit-edge great rhombicuboctahedral prism)
Edge lengthsRemaining edges from class being alternated (24): 1
 Edges from diagonals of original squares (24+24):
 Edges of equilateral triangles (48):
 Long edges of rectangles (24):
Circumradius
Central density1
Related polytopes
ArmyPysna
RegimentPysna
DualPyritosnub altertegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(B3/2×2×A1)/2, order 48
ConvexYes
NatureTame

The pyritosnub alterprism, also known as the edge-snub octahedral hosochoron or pysna, is a convex isogonal polychoron that consists of 2 pyritosnub cubes, 6 rectangular trapezoprisms, 8 triangular gyroprisms, and 24 skewed wedges. 3 wedges, 1 pyritosnub cube, 1 triangular gyroprism, and 1 rectangular trapezoprism join at each vertex. It can be obtained through the process of alternating one class of edges of the great rhombicuboctahedral prism, such that the octagons turn into rectangles. However, it cannot be made uniform, as it generally has up to 5 edge lengths, which can be minimized to no more than 2 different sizes.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:a ≈ 1:1.30910, where a is the largest real root of 13x4-24x3-6x2+16x+5.

Vertex coordinates[edit | edit source]

Vertex coordinates for a pyritosnub alterprism created from the vertices of a great rhombicuboctahedral prism of edge length 1, are given by all even permutations of the first three coordinates of:

A variant where the triangular antiprisms being regular octahedra that are a unit distance apart, centered at the origin, is given by the cyclic permutations excluding the last coordinate of:

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by the cyclic permutations excluding the last coordinate of:

where


External links[edit | edit source]