Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,3}

Atlas Canonical Name {6,3}*1452

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1452,22)
Rank
3
Schläfli Type
{6,3}
Vertices, edges, …
242, 363, 121
Order of s0s1s2
22
Order of s0s1s2s1
6
Also known as
{6,3}(11,0), {6,3}22. if this polytope has another name.

Special Properties

  • Toroidal
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

No regular quotients.

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*s1)^2*s0*s2*s1*s0*s1*s2> of order 11

11 facets

22 vertex figures

P/N, where N=<(s0*s1)^2*(s2*(s1*s0)^2)^2*s2*s1> of order 11

11 facets

22 vertex figures

Representations

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

References

None.

to this polytope.

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