Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,22}

Atlas Canonical Name {3,22}*1452

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1452,22)
Rank
3
Schläfli Type
{3,22}
Vertices, edges, …
33, 363, 242
Order of s0s1s2
6
Order of s0s1s2s1
22
Also known as
{3,22}6. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

121-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*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s2> of order 11

22 facets

3 vertex figures

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

22 facets

13 vertex figures

P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*(s2*s1)^3*s0*s2> of order 11

22 facets

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

References

None.

to this polytope.

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