Polytope of Type {8,58}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,58}*928
Also Known As : {8,58|2}. if this polytope has another name.
Group : SmallGroup(928,131)
Rank : 3
Schlafli Type : {8,58}
Number of vertices, edges, etc : 8, 232, 58
Order of s₀s₁s₂ : 232
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,58,2} of size 1856
Vertex Figure Of :
   {2,8,58} of size 1856
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,58}*464
   4-fold quotients : {2,58}*232
   8-fold quotients : {2,29}*116
   29-fold quotients : {8,2}*32
   58-fold quotients : {4,2}*16
   116-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,116}*1856a, {16,58}*1856
Permutation Representation (GAP) :

s0 := ( 59, 88)( 60, 89)( 61, 90)( 62, 91)( 63, 92)( 64, 93)( 65, 94)( 66, 95)
( 67, 96)( 68, 97)( 69, 98)( 70, 99)( 71,100)( 72,101)( 73,102)( 74,103)
( 75,104)( 76,105)( 77,106)( 78,107)( 79,108)( 80,109)( 81,110)( 82,111)
( 83,112)( 84,113)( 85,114)( 86,115)( 87,116)(117,175)(118,176)(119,177)
(120,178)(121,179)(122,180)(123,181)(124,182)(125,183)(126,184)(127,185)
(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)
(136,194)(137,195)(138,196)(139,197)(140,198)(141,199)(142,200)(143,201)
(144,202)(145,203)(146,204)(147,205)(148,206)(149,207)(150,208)(151,209)
(152,210)(153,211)(154,212)(155,213)(156,214)(157,215)(158,216)(159,217)
(160,218)(161,219)(162,220)(163,221)(164,222)(165,223)(166,224)(167,225)
(168,226)(169,227)(170,228)(171,229)(172,230)(173,231)(174,232);;
s1 := (  1,117)(  2,145)(  3,144)(  4,143)(  5,142)(  6,141)(  7,140)(  8,139)
(  9,138)( 10,137)( 11,136)( 12,135)( 13,134)( 14,133)( 15,132)( 16,131)
( 17,130)( 18,129)( 19,128)( 20,127)( 21,126)( 22,125)( 23,124)( 24,123)
( 25,122)( 26,121)( 27,120)( 28,119)( 29,118)( 30,146)( 31,174)( 32,173)
( 33,172)( 34,171)( 35,170)( 36,169)( 37,168)( 38,167)( 39,166)( 40,165)
( 41,164)( 42,163)( 43,162)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)
( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)
( 57,148)( 58,147)( 59,204)( 60,232)( 61,231)( 62,230)( 63,229)( 64,228)
( 65,227)( 66,226)( 67,225)( 68,224)( 69,223)( 70,222)( 71,221)( 72,220)
( 73,219)( 74,218)( 75,217)( 76,216)( 77,215)( 78,214)( 79,213)( 80,212)
( 81,211)( 82,210)( 83,209)( 84,208)( 85,207)( 86,206)( 87,205)( 88,175)
( 89,203)( 90,202)( 91,201)( 92,200)( 93,199)( 94,198)( 95,197)( 96,196)
( 97,195)( 98,194)( 99,193)(100,192)(101,191)(102,190)(103,189)(104,188)
(105,187)(106,186)(107,185)(108,184)(109,183)(110,182)(111,181)(112,180)
(113,179)(114,178)(115,177)(116,176);;
s2 := (  1,  2)(  3, 29)(  4, 28)(  5, 27)(  6, 26)(  7, 25)(  8, 24)(  9, 23)
( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 30, 31)( 32, 58)
( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)( 40, 50)
( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)( 63, 85)
( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)
( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)( 94,112)
( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)(102,104)
(117,118)(119,145)(120,144)(121,143)(122,142)(123,141)(124,140)(125,139)
(126,138)(127,137)(128,136)(129,135)(130,134)(131,133)(146,147)(148,174)
(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,167)(156,166)
(157,165)(158,164)(159,163)(160,162)(175,176)(177,203)(178,202)(179,201)
(180,200)(181,199)(182,198)(183,197)(184,196)(185,195)(186,194)(187,193)
(188,192)(189,191)(204,205)(206,232)(207,231)(208,230)(209,229)(210,228)
(211,227)(212,226)(213,225)(214,224)(215,223)(216,222)(217,221)(218,220);;
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*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(232)!( 59, 88)( 60, 89)( 61, 90)( 62, 91)( 63, 92)( 64, 93)( 65, 94)
( 66, 95)( 67, 96)( 68, 97)( 69, 98)( 70, 99)( 71,100)( 72,101)( 73,102)
( 74,103)( 75,104)( 76,105)( 77,106)( 78,107)( 79,108)( 80,109)( 81,110)
( 82,111)( 83,112)( 84,113)( 85,114)( 86,115)( 87,116)(117,175)(118,176)
(119,177)(120,178)(121,179)(122,180)(123,181)(124,182)(125,183)(126,184)
(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)
(135,193)(136,194)(137,195)(138,196)(139,197)(140,198)(141,199)(142,200)
(143,201)(144,202)(145,203)(146,204)(147,205)(148,206)(149,207)(150,208)
(151,209)(152,210)(153,211)(154,212)(155,213)(156,214)(157,215)(158,216)
(159,217)(160,218)(161,219)(162,220)(163,221)(164,222)(165,223)(166,224)
(167,225)(168,226)(169,227)(170,228)(171,229)(172,230)(173,231)(174,232);
s1 := Sym(232)!(  1,117)(  2,145)(  3,144)(  4,143)(  5,142)(  6,141)(  7,140)
(  8,139)(  9,138)( 10,137)( 11,136)( 12,135)( 13,134)( 14,133)( 15,132)
( 16,131)( 17,130)( 18,129)( 19,128)( 20,127)( 21,126)( 22,125)( 23,124)
( 24,123)( 25,122)( 26,121)( 27,120)( 28,119)( 29,118)( 30,146)( 31,174)
( 32,173)( 33,172)( 34,171)( 35,170)( 36,169)( 37,168)( 38,167)( 39,166)
( 40,165)( 41,164)( 42,163)( 43,162)( 44,161)( 45,160)( 46,159)( 47,158)
( 48,157)( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)
( 56,149)( 57,148)( 58,147)( 59,204)( 60,232)( 61,231)( 62,230)( 63,229)
( 64,228)( 65,227)( 66,226)( 67,225)( 68,224)( 69,223)( 70,222)( 71,221)
( 72,220)( 73,219)( 74,218)( 75,217)( 76,216)( 77,215)( 78,214)( 79,213)
( 80,212)( 81,211)( 82,210)( 83,209)( 84,208)( 85,207)( 86,206)( 87,205)
( 88,175)( 89,203)( 90,202)( 91,201)( 92,200)( 93,199)( 94,198)( 95,197)
( 96,196)( 97,195)( 98,194)( 99,193)(100,192)(101,191)(102,190)(103,189)
(104,188)(105,187)(106,186)(107,185)(108,184)(109,183)(110,182)(111,181)
(112,180)(113,179)(114,178)(115,177)(116,176);
s2 := Sym(232)!(  1,  2)(  3, 29)(  4, 28)(  5, 27)(  6, 26)(  7, 25)(  8, 24)
(  9, 23)( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 30, 31)
( 32, 58)( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)
( 40, 50)( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)
( 63, 85)( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)
( 71, 77)( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)
( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)
(102,104)(117,118)(119,145)(120,144)(121,143)(122,142)(123,141)(124,140)
(125,139)(126,138)(127,137)(128,136)(129,135)(130,134)(131,133)(146,147)
(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,167)
(156,166)(157,165)(158,164)(159,163)(160,162)(175,176)(177,203)(178,202)
(179,201)(180,200)(181,199)(182,198)(183,197)(184,196)(185,195)(186,194)
(187,193)(188,192)(189,191)(204,205)(206,232)(207,231)(208,230)(209,229)
(210,228)(211,227)(212,226)(213,225)(214,224)(215,223)(216,222)(217,221)
(218,220);
poly := sub<Sym(232)|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*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope