Sphenoverted penteractipenteractitriacontaditeron

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Sphenoverted penteractipenteractitriacontaditeron
Rank5
TypeUniform
Notation
Bowers style acronymWavinant
Coxeter diagramo3o3x3o4x4/3*c ()
Elements
Tera32 rectified pentachora, 10 quasitruncated tesseracts, 10 sphenoverted tesseractitesseractihexadecachora
Cells160 tetrahedra, 160 octahedra, 80 quasitruncated hexahedra, 40 great cubicuboctahedra
Faces320+640 triangles, 80 squares, 240 octagrams
Edges320+960
Vertices320
Vertex figureTriangular pyramidal prism, edge lengths 1 (base triangular prism), 2 (top edge), and 2–2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesQuitit–tet–rap:
 Wavitoth–gocco–wavitoth: 90°
 Wavitoth–quith–quitit: 90°
 Wavitoth–oct–rap:
Related polytopes
ArmySpan, edge length
RegimentWavinant
ConjugateRetrosphenary penteract
Abstract & topological properties
Flag count61440
OrientableYes
Properties
SymmetryB5, order 3840
ConvexNo
NatureTame

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]