Polytope of Type {8,52} with group SmallGroup(832,449)

Overview

Group: SmallGroup(832,449)
Rank: 3
Schläfli Type: {8,52}
Vertices, edges, …: 8, 208, 52
Order of s₀s₁s₂: 104
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{4,52}*416

4-fold

8-fold

{2,26}*104

13-fold

{8,4}*64b

16-fold

{2,13}*52

26-fold

{4,4}*32

52-fold

104-fold

{2,2}*8

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 27, 40)( 28, 41)( 29, 42)( 30, 43)( 31, 44)( 32, 45)( 33, 46)( 34, 47)( 35, 48)( 36, 49)( 37, 50)( 38, 51)( 39, 52)( 53, 66)( 54, 67)( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)( 63, 76)( 64, 77)( 65, 78)(105,131)(106,132)(107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(113,139)(114,140)(115,141)(116,142)(117,143)(118,144)(119,145)(120,146)(121,147)(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,155)(130,156)(157,196)(158,197)(159,198)(160,199)(161,200)(162,201)(163,202)(164,203)(165,204)(166,205)(167,206)(168,207)(169,208)(170,183)(171,184)(172,185)(173,186)(174,187)(175,188)(176,189)(177,190)(178,191)(179,192)(180,193)(181,194)(182,195);;
s1 := (  1,105)(  2,117)(  3,116)(  4,115)(  5,114)(  6,113)(  7,112)(  8,111)(  9,110)( 10,109)( 11,108)( 12,107)( 13,106)( 14,118)( 15,130)( 16,129)( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)( 24,121)( 25,120)( 26,119)( 27,144)( 28,156)( 29,155)( 30,154)( 31,153)( 32,152)( 33,151)( 34,150)( 35,149)( 36,148)( 37,147)( 38,146)( 39,145)( 40,131)( 41,143)( 42,142)( 43,141)( 44,140)( 45,139)( 46,138)( 47,137)( 48,136)( 49,135)( 50,134)( 51,133)( 52,132)( 53,157)( 54,169)( 55,168)( 56,167)( 57,166)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)( 64,159)( 65,158)( 66,170)( 67,182)( 68,181)( 69,180)( 70,179)( 71,178)( 72,177)( 73,176)( 74,175)( 75,174)( 76,173)( 77,172)( 78,171)( 79,196)( 80,208)( 81,207)( 82,206)( 83,205)( 84,204)( 85,203)( 86,202)( 87,201)( 88,200)( 89,199)( 90,198)( 91,197)( 92,183)( 93,195)( 94,194)( 95,193)( 96,192)( 97,191)( 98,190)( 99,189)(100,188)(101,187)(102,186)(103,185)(104,184);;
s2 := (  1,  2)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 15)( 16, 26)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 41)( 28, 40)( 29, 52)( 30, 51)( 31, 50)( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 93)( 80, 92)( 81,104)( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)(105,158)(106,157)(107,169)(108,168)(109,167)(110,166)(111,165)(112,164)(113,163)(114,162)(115,161)(116,160)(117,159)(118,171)(119,170)(120,182)(121,181)(122,180)(123,179)(124,178)(125,177)(126,176)(127,175)(128,174)(129,173)(130,172)(131,197)(132,196)(133,208)(134,207)(135,206)(136,205)(137,204)(138,203)(139,202)(140,201)(141,200)(142,199)(143,198)(144,184)(145,183)(146,195)(147,194)(148,193)(149,192)(150,191)(151,190)(152,189)(153,188)(154,187)(155,186)(156,185);;
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*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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(208)!( 27, 40)( 28, 41)( 29, 42)( 30, 43)( 31, 44)( 32, 45)( 33, 46)( 34, 47)( 35, 48)( 36, 49)( 37, 50)( 38, 51)( 39, 52)( 53, 66)( 54, 67)( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)( 63, 76)( 64, 77)( 65, 78)(105,131)(106,132)(107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(113,139)(114,140)(115,141)(116,142)(117,143)(118,144)(119,145)(120,146)(121,147)(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,155)(130,156)(157,196)(158,197)(159,198)(160,199)(161,200)(162,201)(163,202)(164,203)(165,204)(166,205)(167,206)(168,207)(169,208)(170,183)(171,184)(172,185)(173,186)(174,187)(175,188)(176,189)(177,190)(178,191)(179,192)(180,193)(181,194)(182,195);
s1 := Sym(208)!(  1,105)(  2,117)(  3,116)(  4,115)(  5,114)(  6,113)(  7,112)(  8,111)(  9,110)( 10,109)( 11,108)( 12,107)( 13,106)( 14,118)( 15,130)( 16,129)( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)( 24,121)( 25,120)( 26,119)( 27,144)( 28,156)( 29,155)( 30,154)( 31,153)( 32,152)( 33,151)( 34,150)( 35,149)( 36,148)( 37,147)( 38,146)( 39,145)( 40,131)( 41,143)( 42,142)( 43,141)( 44,140)( 45,139)( 46,138)( 47,137)( 48,136)( 49,135)( 50,134)( 51,133)( 52,132)( 53,157)( 54,169)( 55,168)( 56,167)( 57,166)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)( 64,159)( 65,158)( 66,170)( 67,182)( 68,181)( 69,180)( 70,179)( 71,178)( 72,177)( 73,176)( 74,175)( 75,174)( 76,173)( 77,172)( 78,171)( 79,196)( 80,208)( 81,207)( 82,206)( 83,205)( 84,204)( 85,203)( 86,202)( 87,201)( 88,200)( 89,199)( 90,198)( 91,197)( 92,183)( 93,195)( 94,194)( 95,193)( 96,192)( 97,191)( 98,190)( 99,189)(100,188)(101,187)(102,186)(103,185)(104,184);
s2 := Sym(208)!(  1,  2)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 15)( 16, 26)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 41)( 28, 40)( 29, 52)( 30, 51)( 31, 50)( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 93)( 80, 92)( 81,104)( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)(105,158)(106,157)(107,169)(108,168)(109,167)(110,166)(111,165)(112,164)(113,163)(114,162)(115,161)(116,160)(117,159)(118,171)(119,170)(120,182)(121,181)(122,180)(123,179)(124,178)(125,177)(126,176)(127,175)(128,174)(129,173)(130,172)(131,197)(132,196)(133,208)(134,207)(135,206)(136,205)(137,204)(138,203)(139,202)(140,201)(141,200)(142,199)(143,198)(144,184)(145,183)(146,195)(147,194)(148,193)(149,192)(150,191)(151,190)(152,189)(153,188)(154,187)(155,186)(156,185);
poly := sub<Sym(208)|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*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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