Polytope of Type {2,58,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,58,8}*1856
if this polytope has a name.
Group : SmallGroup(1856,1317)
Rank : 4
Schlafli Type : {2,58,8}
Number of vertices, edges, etc : 2, 58, 232, 8
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 : {2,58,4}*928
   4-fold quotients : {2,58,2}*464
   8-fold quotients : {2,29,2}*232
   29-fold quotients : {2,2,8}*64
   58-fold quotients : {2,2,4}*32
   116-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope