Frustosphenary dispenteractitriacontaditeron

Frustosphenary dispenteractitriacontaditeron
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Fawdint
Coxeter diagram	o3x3o3o *b4/3x4*c ()
Elements
Tera	32 rectified pentachora, 10 great tesseractitesseractihexadecachora, 10 sphenoverted tesseractitesseractihexadecachora
Cells	160 tetrahedra, 160 octahedra, 40 cubes, 40 quasitruncated hexahedra, 80 great cubicuboctahedra
Faces	320+640 triangles, 240 squares, 240 octagrams
Edges	480+960
Vertices	320
Vertex figure	Triangular fastegium, edge lengths 1 (base triangular prism), √2 (top triangle), and √2–√2 (sides)
Measures (edge length 1)
Circumradius	${\frac {2{\sqrt {2}}-1}{2}}\approx 0.91421$
Hypervolume	${\frac {670-407{\sqrt {2}}}{30}}\approx 3.14715$
Diteral angles	Wavitoth–oct–rap: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Gittith–cube–gittith: 90°
	Wavitoth–quith–wavitoth: 90°
	Gittith–gocco–wavitoth: 90°
	Gittith–tet–rap: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
Related polytopes
Army	Sirn, edge length ${\sqrt {2}}-1$
Regiment	Fawdint
Conjugate	Small retroprismated penteract
Abstract & topological properties
Flag count	69120
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	No
Nature	Tame

The frustosphenary dispenteractitriacontaditeron, or fawdint, is a nonconvex uniform polyteron. It consists of 10 sphenoverted tesseractitesseractihexadecachora, 10 great tesseractitesseractihexadecachora, and 32 rectified pentachora. 3 sphenoverted tesseractitesseractihexadecachora, 2 great tesseractitesseractihexadecachora, and 1 rectified pentachoron join at each vertex.

The frustosphenary dispenteractitriacontaditeron contains the vertices of a sphenoverted tesseractitesseractihexadecachoric prism, square-quasitruncated hexahedral duoprism, octagrammic-great cubicuboctahedral duoprism, and octagrammic duoprismatic prism.

Vertex coordinates

The vertices of a frustosphenary dispenteractitriacontaditeron of edge length 1 are given by all permutations of:

• $\left(\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right).$

Related polytopes

The regiment of the frustosphenary dispenteractitriacontaditeron includes a total of 37 members plus one fissary member.

External links

• Klitzing, Richard. "fawdint".