Rank8
TypeScaliform
Elements
Zetta
Exa
Peta
Tera
Cells26880+107520+107520+430080 tetrahedra
Faces107520+215040 triangles
Edges53760
Vertices1920
Vertex figureOctadiminished 7-demicube, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {2}}\approx 1.41421}$
Central density1
Number of external pieces2400
Related polytopes
ConjugateNone
Abstract & topological properties
Flag count2136637440
Euler characteristic0
OrientableYes
Properties
ConvexYes
NatureTame

The diacositetracontadiminished 241 polytope or diacositetracontadiminished diacositetraconta-myriaheptachiliadiacosioctaconta-zetton, abbreviated as 240-diminished 240-17280-zetton, is a convex scaliform 8-polytope. It has 1920 7-simplices, 240 7-demicubes and 240 hepteractidiminished 231 polytopes as facets. Eight 7-simplices, eight 7-demicubes, and 14 hepteractidiminished 231 polytopes meet each vertex.

One can create this polyzetton by removing an inscribed 421 polytope's vertices from the 241 polytope.

## Vertex coordinates

The vertices of a diacositetracontadiminished 241 polytope of edge length 1, centered at the origin, are given by:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,0,\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,0,\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm 1,\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,0,\,\pm 1\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1\right)}$,
• ${\displaystyle \left(\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0\right)}$,
• ${\displaystyle \left(0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0\right)}$,
• ${\displaystyle \left(0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0\right)}$,
• ${\displaystyle \left(0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1\right)}$,
• ${\displaystyle \left(\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0\right)}$,
• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0\right)}$,
• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0\right)}$,
• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1\right)}$,
• ${\displaystyle \left(\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0\right)}$,
• $\displaystyle \left(0 ,\, \pm \frac12 ,\, \pm \frac12 ,\, \pm 1 ,\, 0 ,\, \pm \frac12 ,\, \pm \frac12 ,\, 0\right)$ ,
• $\displaystyle \left(0 ,\, \pm \frac12 ,\, \pm \frac12 ,\, 0 ,\, \pm 1 ,\, \pm \frac12 ,\, \pm \frac12 ,\, 0\right)$ ,
• $\displaystyle \left(0 ,\, \pm \frac12 ,\, \pm \frac12 ,\, 0 ,\, 0 ,\, \pm \frac12 ,\, \pm \frac12 ,\, \pm 1\right)$ ,
• $\displaystyle \left(\pm \frac12 ,\, \pm 1 ,\, 0 ,\, \pm \frac12 ,\, 0 ,\, \pm \frac12 ,\, \pm \frac12 ,\, 0\right)$ ,
• $\displaystyle \left(\pm \frac12 ,\, 0 ,\, \pm 1 ,\, \pm \frac12 ,\, 0 ,\, \pm \frac12 ,\, \pm \frac12 ,\, 0\right)$ ,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1\right)}$,
• ${\displaystyle \left(\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm 1,\,0,\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,\pm 1,\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,0,\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(0,\,0,\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left({\frac {1}{2}},\,{\frac {1}{2}},\,{\frac {1}{2}},\,{\frac {1}{2}},\,{\frac {1}{2}},\,{\frac {1}{2}},\,{\frac {1}{2}},\,{\frac {1}{2}}\right)}$ and all odd sign changes.