Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,92}

Atlas Canonical Name {6,92}*1656

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Overview

Group
SmallGroup(1656,113)
Rank
3
Schläfli Type
{6,92}
Vertices, edges, …
9, 414, 138
Order of s0s1s2
92
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

23-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := ( 24, 47)( 25, 48)( 26, 49)( 27, 50)( 28, 51)( 29, 52)( 30, 53)( 31, 54)( 32, 55)( 33, 56)( 34, 57)( 35, 58)( 36, 59)( 37, 60)( 38, 61)( 39, 62)( 40, 63)( 41, 64)( 42, 65)( 43, 66)( 44, 67)( 45, 68)( 46, 69)( 70,139)( 71,140)( 72,141)( 73,142)( 74,143)( 75,144)( 76,145)( 77,146)( 78,147)( 79,148)( 80,149)( 81,150)( 82,151)( 83,152)( 84,153)( 85,154)( 86,155)( 87,156)( 88,157)( 89,158)( 90,159)( 91,160)( 92,161)( 93,185)( 94,186)( 95,187)( 96,188)( 97,189)( 98,190)( 99,191)(100,192)(101,193)(102,194)(103,195)(104,196)(105,197)(106,198)(107,199)(108,200)(109,201)(110,202)(111,203)(112,204)(113,205)(114,206)(115,207)(116,162)(117,163)(118,164)(119,165)(120,166)(121,167)(122,168)(123,169)(124,170)(125,171)(126,172)(127,173)(128,174)(129,175)(130,176)(131,177)(132,178)(133,179)(134,180)(135,181)(136,182)(137,183)(138,184);;
s1 := (  1, 70)(  2, 92)(  3, 91)(  4, 90)(  5, 89)(  6, 88)(  7, 87)(  8, 86)(  9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14, 80)( 15, 79)( 16, 78)( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)( 24, 93)( 25,115)( 26,114)( 27,113)( 28,112)( 29,111)( 30,110)( 31,109)( 32,108)( 33,107)( 34,106)( 35,105)( 36,104)( 37,103)( 38,102)( 39,101)( 40,100)( 41, 99)( 42, 98)( 43, 97)( 44, 96)( 45, 95)( 46, 94)( 47,116)( 48,138)( 49,137)( 50,136)( 51,135)( 52,134)( 53,133)( 54,132)( 55,131)( 56,130)( 57,129)( 58,128)( 59,127)( 60,126)( 61,125)( 62,124)( 63,123)( 64,122)( 65,121)( 66,120)( 67,119)( 68,118)( 69,117)(140,161)(141,160)(142,159)(143,158)(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)(163,184)(164,183)(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)(173,174)(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197);;
s2 := (  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 24, 71)( 25, 70)( 26, 92)( 27, 91)( 28, 90)( 29, 89)( 30, 88)( 31, 87)( 32, 86)( 33, 85)( 34, 84)( 35, 83)( 36, 82)( 37, 81)( 38, 80)( 39, 79)( 40, 78)( 41, 77)( 42, 76)( 43, 75)( 44, 74)( 45, 73)( 46, 72)( 47,140)( 48,139)( 49,161)( 50,160)( 51,159)( 52,158)( 53,157)( 54,156)( 55,155)( 56,154)( 57,153)( 58,152)( 59,151)( 60,150)( 61,149)( 62,148)( 63,147)( 64,146)( 65,145)( 66,144)( 67,143)( 68,142)( 69,141)( 93, 94)( 95,115)( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(101,109)(102,108)(103,107)(104,106)(116,163)(117,162)(118,184)(119,183)(120,182)(121,181)(122,180)(123,179)(124,178)(125,177)(126,176)(127,175)(128,174)(129,173)(130,172)(131,171)(132,170)(133,169)(134,168)(135,167)(136,166)(137,165)(138,164)(185,186)(187,207)(188,206)(189,205)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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*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(207)!( 24, 47)( 25, 48)( 26, 49)( 27, 50)( 28, 51)( 29, 52)( 30, 53)( 31, 54)( 32, 55)( 33, 56)( 34, 57)( 35, 58)( 36, 59)( 37, 60)( 38, 61)( 39, 62)( 40, 63)( 41, 64)( 42, 65)( 43, 66)( 44, 67)( 45, 68)( 46, 69)( 70,139)( 71,140)( 72,141)( 73,142)( 74,143)( 75,144)( 76,145)( 77,146)( 78,147)( 79,148)( 80,149)( 81,150)( 82,151)( 83,152)( 84,153)( 85,154)( 86,155)( 87,156)( 88,157)( 89,158)( 90,159)( 91,160)( 92,161)( 93,185)( 94,186)( 95,187)( 96,188)( 97,189)( 98,190)( 99,191)(100,192)(101,193)(102,194)(103,195)(104,196)(105,197)(106,198)(107,199)(108,200)(109,201)(110,202)(111,203)(112,204)(113,205)(114,206)(115,207)(116,162)(117,163)(118,164)(119,165)(120,166)(121,167)(122,168)(123,169)(124,170)(125,171)(126,172)(127,173)(128,174)(129,175)(130,176)(131,177)(132,178)(133,179)(134,180)(135,181)(136,182)(137,183)(138,184);
s1 := Sym(207)!(  1, 70)(  2, 92)(  3, 91)(  4, 90)(  5, 89)(  6, 88)(  7, 87)(  8, 86)(  9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14, 80)( 15, 79)( 16, 78)( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)( 24, 93)( 25,115)( 26,114)( 27,113)( 28,112)( 29,111)( 30,110)( 31,109)( 32,108)( 33,107)( 34,106)( 35,105)( 36,104)( 37,103)( 38,102)( 39,101)( 40,100)( 41, 99)( 42, 98)( 43, 97)( 44, 96)( 45, 95)( 46, 94)( 47,116)( 48,138)( 49,137)( 50,136)( 51,135)( 52,134)( 53,133)( 54,132)( 55,131)( 56,130)( 57,129)( 58,128)( 59,127)( 60,126)( 61,125)( 62,124)( 63,123)( 64,122)( 65,121)( 66,120)( 67,119)( 68,118)( 69,117)(140,161)(141,160)(142,159)(143,158)(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)(163,184)(164,183)(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)(173,174)(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197);
s2 := Sym(207)!(  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 24, 71)( 25, 70)( 26, 92)( 27, 91)( 28, 90)( 29, 89)( 30, 88)( 31, 87)( 32, 86)( 33, 85)( 34, 84)( 35, 83)( 36, 82)( 37, 81)( 38, 80)( 39, 79)( 40, 78)( 41, 77)( 42, 76)( 43, 75)( 44, 74)( 45, 73)( 46, 72)( 47,140)( 48,139)( 49,161)( 50,160)( 51,159)( 52,158)( 53,157)( 54,156)( 55,155)( 56,154)( 57,153)( 58,152)( 59,151)( 60,150)( 61,149)( 62,148)( 63,147)( 64,146)( 65,145)( 66,144)( 67,143)( 68,142)( 69,141)( 93, 94)( 95,115)( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(101,109)(102,108)(103,107)(104,106)(116,163)(117,162)(118,184)(119,183)(120,182)(121,181)(122,180)(123,179)(124,178)(125,177)(126,176)(127,175)(128,174)(129,173)(130,172)(131,171)(132,170)(133,169)(134,168)(135,167)(136,166)(137,165)(138,164)(185,186)(187,207)(188,206)(189,205)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198);
poly := sub<Sym(207)|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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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*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.

Twisty Puzzle