Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,4}

Atlas Canonical Name {10,4}*1280b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1280,1116454)
Rank
3
Schläfli Type
{10,4}
Vertices, edges, …
160, 320, 64
Order of s0s1s2
20
Order of s0s1s2s1
8
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

32-fold

64-fold

160-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*s2*s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 2

32 facets

80 vertex figures

P/N, where N=<s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1> of order 2

32 facets

88 vertex figures

P/N, where N=<(s0*s2*s1)^2*s0*s2*(s1*s0)^2*s2*s1*s2> of order 2

32 facets

80 vertex figures

P/N, where N=<(s1*s0)^3*s2*s1*s0*s1*s2> of order 4

16 facets

44 vertex figures

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2> of order 4

16 facets

44 vertex figures

P/N, where N=<s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s0*s2*s1*s2> of order 4

16 facets

44 vertex figures

P/N, where N=<s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1, s0*s1*(s2*s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 4

16 facets

44 vertex figures

Representations

Permutation Representation (GAP) 
s0 := (  3,  4)(  7,  8)( 11, 12)( 15, 16)( 17, 26)( 18, 25)( 19, 27)( 20, 28)( 21, 30)( 22, 29)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 49, 50)( 53, 54)( 57, 58)( 61, 62)( 65,121)( 66,122)( 67,124)( 68,123)( 69,125)( 70,126)( 71,128)( 72,127)( 73,113)( 74,114)( 75,116)( 76,115)( 77,117)( 78,118)( 79,120)( 80,119)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,105)( 90,106)( 91,108)( 92,107)( 93,109)( 94,110)( 95,112)( 96,111);;
s1 := (  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9,102)( 10,101)( 11,103)( 12,104)( 13, 98)( 14, 97)( 15, 99)( 16,100)( 17, 62)( 18, 61)( 19, 63)( 20, 64)( 21, 58)( 22, 57)( 23, 59)( 24, 60)( 25, 94)( 26, 93)( 27, 95)( 28, 96)( 29, 90)( 30, 89)( 31, 91)( 32, 92)( 33, 78)( 34, 77)( 35, 79)( 36, 80)( 37, 74)( 38, 73)( 39, 75)( 40, 76)( 41, 46)( 42, 45)( 43, 47)( 44, 48)( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)( 56,115)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 81,126)( 82,125)( 83,127)( 84,128)( 85,122)( 86,121)( 87,123)( 88,124)(105,110)(106,109)(107,111)(108,112);;
s2 := (  1, 51)(  2, 52)(  3, 50)(  4, 49)(  5, 55)(  6, 56)(  7, 54)(  8, 53)(  9, 59)( 10, 60)( 11, 58)( 12, 57)( 13, 63)( 14, 64)( 15, 62)( 16, 61)( 17, 35)( 18, 36)( 19, 34)( 20, 33)( 21, 39)( 22, 40)( 23, 38)( 24, 37)( 25, 43)( 26, 44)( 27, 42)( 28, 41)( 29, 47)( 30, 48)( 31, 46)( 32, 45)( 65,115)( 66,116)( 67,114)( 68,113)( 69,119)( 70,120)( 71,118)( 72,117)( 73,123)( 74,124)( 75,122)( 76,121)( 77,127)( 78,128)( 79,126)( 80,125)( 81, 99)( 82,100)( 83, 98)( 84, 97)( 85,103)( 86,104)( 87,102)( 88,101)( 89,107)( 90,108)( 91,106)( 92,105)( 93,111)( 94,112)( 95,110)( 96,109);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(128)!(  3,  4)(  7,  8)( 11, 12)( 15, 16)( 17, 26)( 18, 25)( 19, 27)( 20, 28)( 21, 30)( 22, 29)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 49, 50)( 53, 54)( 57, 58)( 61, 62)( 65,121)( 66,122)( 67,124)( 68,123)( 69,125)( 70,126)( 71,128)( 72,127)( 73,113)( 74,114)( 75,116)( 76,115)( 77,117)( 78,118)( 79,120)( 80,119)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,105)( 90,106)( 91,108)( 92,107)( 93,109)( 94,110)( 95,112)( 96,111);
s1 := Sym(128)!(  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9,102)( 10,101)( 11,103)( 12,104)( 13, 98)( 14, 97)( 15, 99)( 16,100)( 17, 62)( 18, 61)( 19, 63)( 20, 64)( 21, 58)( 22, 57)( 23, 59)( 24, 60)( 25, 94)( 26, 93)( 27, 95)( 28, 96)( 29, 90)( 30, 89)( 31, 91)( 32, 92)( 33, 78)( 34, 77)( 35, 79)( 36, 80)( 37, 74)( 38, 73)( 39, 75)( 40, 76)( 41, 46)( 42, 45)( 43, 47)( 44, 48)( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)( 56,115)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 81,126)( 82,125)( 83,127)( 84,128)( 85,122)( 86,121)( 87,123)( 88,124)(105,110)(106,109)(107,111)(108,112);
s2 := Sym(128)!(  1, 51)(  2, 52)(  3, 50)(  4, 49)(  5, 55)(  6, 56)(  7, 54)(  8, 53)(  9, 59)( 10, 60)( 11, 58)( 12, 57)( 13, 63)( 14, 64)( 15, 62)( 16, 61)( 17, 35)( 18, 36)( 19, 34)( 20, 33)( 21, 39)( 22, 40)( 23, 38)( 24, 37)( 25, 43)( 26, 44)( 27, 42)( 28, 41)( 29, 47)( 30, 48)( 31, 46)( 32, 45)( 65,115)( 66,116)( 67,114)( 68,113)( 69,119)( 70,120)( 71,118)( 72,117)( 73,123)( 74,124)( 75,122)( 76,121)( 77,127)( 78,128)( 79,126)( 80,125)( 81, 99)( 82,100)( 83, 98)( 84, 97)( 85,103)( 86,104)( 87,102)( 88,101)( 89,107)( 90,108)( 91,106)( 92,105)( 93,111)( 94,112)( 95,110)( 96,109);
poly := sub<Sym(128)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.

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