Polytope of Type {2,8,58}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,58}*1856
if this polytope has a name.
Group : SmallGroup(1856,1317)
Rank : 4
Schlafli Type : {2,8,58}
Number of vertices, edges, etc : 2, 8, 232, 58
Order of s₀s₁s₂s₃ : 232
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,58}*928
   4-fold quotients : {2,2,58}*464
   8-fold quotients : {2,2,29}*232
   29-fold quotients : {2,8,2}*64
   58-fold quotients : {2,4,2}*32
   116-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 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)( 88,117)( 89,118)(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)(175,233)(176,234);;
s2 := (  3,119)(  4,147)(  5,146)(  6,145)(  7,144)(  8,143)(  9,142)( 10,141)
( 11,140)( 12,139)( 13,138)( 14,137)( 15,136)( 16,135)( 17,134)( 18,133)
( 19,132)( 20,131)( 21,130)( 22,129)( 23,128)( 24,127)( 25,126)( 26,125)
( 27,124)( 28,123)( 29,122)( 30,121)( 31,120)( 32,148)( 33,176)( 34,175)
( 35,174)( 36,173)( 37,172)( 38,171)( 39,170)( 40,169)( 41,168)( 42,167)
( 43,166)( 44,165)( 45,164)( 46,163)( 47,162)( 48,161)( 49,160)( 50,159)
( 51,158)( 52,157)( 53,156)( 54,155)( 55,154)( 56,153)( 57,152)( 58,151)
( 59,150)( 60,149)( 61,206)( 62,234)( 63,233)( 64,232)( 65,231)( 66,230)
( 67,229)( 68,228)( 69,227)( 70,226)( 71,225)( 72,224)( 73,223)( 74,222)
( 75,221)( 76,220)( 77,219)( 78,218)( 79,217)( 80,216)( 81,215)( 82,214)
( 83,213)( 84,212)( 85,211)( 86,210)( 87,209)( 88,208)( 89,207)( 90,177)
( 91,205)( 92,204)( 93,203)( 94,202)( 95,201)( 96,200)( 97,199)( 98,198)
( 99,197)(100,196)(101,195)(102,194)(103,193)(104,192)(105,191)(106,190)
(107,189)(108,188)(109,187)(110,186)(111,185)(112,184)(113,183)(114,182)
(115,181)(116,180)(117,179)(118,178);;
s3 := (  3,  4)(  5, 31)(  6, 30)(  7, 29)(  8, 28)(  9, 27)( 10, 26)( 11, 25)
( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 32, 33)( 34, 60)
( 35, 59)( 36, 58)( 37, 57)( 38, 56)( 39, 55)( 40, 54)( 41, 53)( 42, 52)
( 43, 51)( 44, 50)( 45, 49)( 46, 48)( 61, 62)( 63, 89)( 64, 88)( 65, 87)
( 66, 86)( 67, 85)( 68, 84)( 69, 83)( 70, 82)( 71, 81)( 72, 80)( 73, 79)
( 74, 78)( 75, 77)( 90, 91)( 92,118)( 93,117)( 94,116)( 95,115)( 96,114)
( 97,113)( 98,112)( 99,111)(100,110)(101,109)(102,108)(103,107)(104,106)
(119,120)(121,147)(122,146)(123,145)(124,144)(125,143)(126,142)(127,141)
(128,140)(129,139)(130,138)(131,137)(132,136)(133,135)(148,149)(150,176)
(151,175)(152,174)(153,173)(154,172)(155,171)(156,170)(157,169)(158,168)
(159,167)(160,166)(161,165)(162,164)(177,178)(179,205)(180,204)(181,203)
(182,202)(183,201)(184,200)(185,199)(186,198)(187,197)(188,196)(189,195)
(190,194)(191,193)(206,207)(208,234)(209,233)(210,232)(211,231)(212,230)
(213,229)(214,228)(215,227)(216,226)(217,225)(218,224)(219,223)(220,222);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(234)!(1,2);
s1 := Sym(234)!( 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)( 88,117)( 89,118)(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)(175,233)(176,234);
s2 := Sym(234)!(  3,119)(  4,147)(  5,146)(  6,145)(  7,144)(  8,143)(  9,142)
( 10,141)( 11,140)( 12,139)( 13,138)( 14,137)( 15,136)( 16,135)( 17,134)
( 18,133)( 19,132)( 20,131)( 21,130)( 22,129)( 23,128)( 24,127)( 25,126)
( 26,125)( 27,124)( 28,123)( 29,122)( 30,121)( 31,120)( 32,148)( 33,176)
( 34,175)( 35,174)( 36,173)( 37,172)( 38,171)( 39,170)( 40,169)( 41,168)
( 42,167)( 43,166)( 44,165)( 45,164)( 46,163)( 47,162)( 48,161)( 49,160)
( 50,159)( 51,158)( 52,157)( 53,156)( 54,155)( 55,154)( 56,153)( 57,152)
( 58,151)( 59,150)( 60,149)( 61,206)( 62,234)( 63,233)( 64,232)( 65,231)
( 66,230)( 67,229)( 68,228)( 69,227)( 70,226)( 71,225)( 72,224)( 73,223)
( 74,222)( 75,221)( 76,220)( 77,219)( 78,218)( 79,217)( 80,216)( 81,215)
( 82,214)( 83,213)( 84,212)( 85,211)( 86,210)( 87,209)( 88,208)( 89,207)
( 90,177)( 91,205)( 92,204)( 93,203)( 94,202)( 95,201)( 96,200)( 97,199)
( 98,198)( 99,197)(100,196)(101,195)(102,194)(103,193)(104,192)(105,191)
(106,190)(107,189)(108,188)(109,187)(110,186)(111,185)(112,184)(113,183)
(114,182)(115,181)(116,180)(117,179)(118,178);
s3 := Sym(234)!(  3,  4)(  5, 31)(  6, 30)(  7, 29)(  8, 28)(  9, 27)( 10, 26)
( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 32, 33)
( 34, 60)( 35, 59)( 36, 58)( 37, 57)( 38, 56)( 39, 55)( 40, 54)( 41, 53)
( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)( 61, 62)( 63, 89)( 64, 88)
( 65, 87)( 66, 86)( 67, 85)( 68, 84)( 69, 83)( 70, 82)( 71, 81)( 72, 80)
( 73, 79)( 74, 78)( 75, 77)( 90, 91)( 92,118)( 93,117)( 94,116)( 95,115)
( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(101,109)(102,108)(103,107)
(104,106)(119,120)(121,147)(122,146)(123,145)(124,144)(125,143)(126,142)
(127,141)(128,140)(129,139)(130,138)(131,137)(132,136)(133,135)(148,149)
(150,176)(151,175)(152,174)(153,173)(154,172)(155,171)(156,170)(157,169)
(158,168)(159,167)(160,166)(161,165)(162,164)(177,178)(179,205)(180,204)
(181,203)(182,202)(183,201)(184,200)(185,199)(186,198)(187,197)(188,196)
(189,195)(190,194)(191,193)(206,207)(208,234)(209,233)(210,232)(211,231)
(212,230)(213,229)(214,228)(215,227)(216,226)(217,225)(218,224)(219,223)
(220,222);
poly := sub<Sym(234)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope