The diacositetracontadiminished diacositetraconta-myriaheptachiliadiacosioctaconta-zetton , abbreviated as 240-diminished 240-17280-zetton , is a convex scaliform polyzetton . It has 1920 octaexa , 240 demihepteracts and 240 hepteractidiminished pentacontahexapentacosiheptacontahexaexa as facets. 8 octaexa , 8 demihepteracts , and 14 hepteractidiminished pentacontahexapentacosiheptacontahexaexa meet each vertex.
One can create this polyzetton by removing an inscribed 2160-17280-zetton's vertices from a 240-17280-zetton.
The vertices of a diacositetracontadiminished diacositetraconta-myriaheptachiliadiacosioctaconta-zetton of edge length 1, centered at the origin, are given by:
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,0,\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,0,\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm 1,\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,0,\,\pm 1\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1\right),}
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{\displaystyle \left(\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0\right),}
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{\displaystyle \left(0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0\right),}
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{\displaystyle \left(0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0\right),}
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{\displaystyle \left(0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1\right),}
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{\displaystyle \left(\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1\right),}
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{\displaystyle \left(\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1\right),}
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{\displaystyle \left(\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right),}
(
0
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{\displaystyle \left(0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
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1
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0
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±
1
2
)
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
(
±
1
2
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±
1
2
,
0
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0
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±
1
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1
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±
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2
)
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{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
(
±
1
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0
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±
1
2
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±
1
2
,
0
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0
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±
1
2
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±
1
2
)
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{\displaystyle \left(\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
(
0
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±
1
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±
1
2
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±
1
2
,
0
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0
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±
1
2
,
±
1
2
)
,
{\displaystyle \left(0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
(
0
,
0
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±
1
2
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±
1
2
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±
1
,
0
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±
1
2
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±
1
2
)
,
{\displaystyle \left(0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
(
0
,
0
,
±
1
2
,
±
1
2
,
0
,
±
1
,
±
1
2
,
±
1
2
)
,
{\displaystyle \left(0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
(
±
1
,
0
,
0
,
0
,
±
1
2
,
±
1
2
,
±
1
2
,
±
1
2
)
,
{\displaystyle \left(\pm 1,\,0,\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
(
0
,
±
1
,
0
,
0
,
±
1
2
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±
1
2
,
±
1
2
,
±
1
2
)
,
{\displaystyle \left(0,\,\pm 1,\,0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
(
0
,
0
,
±
1
,
0
,
±
1
2
,
±
1
2
,
±
1
2
,
±
1
2
)
,
{\displaystyle \left(0,\,0,\,\pm 1,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
(
0
,
0
,
0
,
±
1
,
±
1
2
,
±
1
2
,
±
1
2
,
±
1
2
)
,
{\displaystyle \left(0,\,0,\,0,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}
(
1
2
,
1
2
,
1
2
,
1
2
,
1
2
,
1
2
,
1
2
,
1
2
)
{\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.