Snub prismatotriacontaditeron

From Polytope Wiki
Jump to navigation Jump to search
Snub prismatotriacontaditeron
File:Snub prismatotriacontaditeron.png
Rank5
TypeIsogonal
Notation
Bowers style acronymSnippit
Coxeter diagrams3s3s3s4o
Elements
Tera960 sphenoidal pyramids, 80 digonal-triangular duoantiprisms, 40 pyritohedral icosahedral antiprisms, 32 snub pentachora, 10 snub rhombatohexadecachora
Cells1920 irregular tetrahedra, 960+960+960 sphenoids, 240+240 tetragonal disphenoids, 80+80 pyritohedral icosahedra, 160 snub tetrahedra, 320+320 triangular gyroprisms
Faces1920+1920+1920 scalene triangles, 960+960+960+960 isosceles triangles, 320+320+640 triangles
Edges480+480+960+960+960+960+1920
Vertices960
Measures (based on uniform great prismated triacontaditeron of edge length 1)
Edge lengthsDiagonals of squares (480+480+960+960):
 Edges of triangles (960+960+1920):
Circumradius
Central density1
Related polytopes
DualTetradecachoric enneacosihexecontateron
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB5/2, order 1920
ConvexYes
NatureTame

The snub prismatotriacontaditeron or snippit, also commonly called the omnisnub demipenteract, is a convex isogonal polyteron that consists of 10 snub rhombatohexadecachora, 32 snub pentachora, 40 pyritohedral icosahedral antiprisms, 80 digonal-triangular duoantiprisms, and 960 sphenoidal pyramids. 1 snub rhombatohexadecachoron, 2 snub pentachora, 1 pyritohedral icosahedral antiprism, 1 digonal-triangular duoantiprism, and 5 sphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the great prismated triacontaditeron. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.21301.

Vertex coordinates[edit | edit source]

The vertices of a snub prismatotriacontaditeron, assuming that the edge length differences are minimized via the absolute value method, centered at the origin, are given by all even permutations and all sign changes of:

Another set of coordinates for a snub prismatotriacontaditeron, using the ratio method, centered at the origin, are given by all even permutations and all sign changes of:

External links[edit | edit source]