Sphenoverted penteractipenteractitriacontaditeron
Sphenoverted penteractipenteractitriacontaditeron | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Wavinant |
Coxeter diagram | o3o3x3o4x4/3*c () |
Elements | |
Tera | 32 rectified pentachora, 10 quasitruncated tesseracts, 10 sphenoverted tesseractitesseractihexadecachora |
Cells | 160 tetrahedra, 160 octahedra, 80 quasitruncated hexahedra, 40 great cubicuboctahedra |
Faces | 320+640 triangles, 80 squares, 240 octagrams |
Edges | 320+960 |
Vertices | 320 |
Vertex figure | Triangular pyramidal prism, edge lengths 1 (base triangular prism), √2 (top edge), and √2–√2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Quitit–tet–rap: |
Wavitoth–gocco–wavitoth: 90° | |
Wavitoth–quith–quitit: 90° | |
Wavitoth–oct–rap: | |
Related polytopes | |
Army | Span, edge length |
Regiment | Wavinant |
Conjugate | Retrosphenary penteract |
Abstract & topological properties | |
Flag count | 61440 |
Orientable | Yes |
Properties | |
Symmetry | B5, order 3840 |
Convex | No |
Nature | Tame |
The sphenoverted penteractipenteractitriacontaditeron, or wavinant, is a nonconvex uniform polyteron. It consists of 10 quasitruncated tesseracts, 10 sphenoverted tesseractitesseractihexadecachora, and 32 rectified pentachora. 3 sphenoverted tesseractitesseractihexadecachora, 2 quasitruncated tesseracts, and 1 rectified pentachoron join at each vertex.
The sphenoverted penteractipenteractitriacontaditeron contains the vertices of a quasitruncated tesseractic prism and octagrammic-quasitruncated hexahedral duoprism.
Vertex coordinates[edit | edit source]
The vertices of a sphenoverted penteractipenteractitriacontaditeron of edge length 1 are given by all permutations of:
Related polytopes[edit | edit source]
The sphenoverted penteractipenteractitriacontaditeron is the colonel of a regiment that includes 15 uniform members.
External links[edit | edit source]
- Klitzing, Richard. "wavinant".