Polytope of Type {58,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {58,8,2}*1856
if this polytope has a name.
Group : SmallGroup(1856,1317)
Rank : 4
Schlafli Type : {58,8,2}
Number of vertices, edges, etc : 58, 232, 8, 2
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 : {58,4,2}*928
   4-fold quotients : {58,2,2}*464
   8-fold quotients : {29,2,2}*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 := (  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)(  9, 22)
( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 31, 58)( 32, 57)
( 33, 56)( 34, 55)( 35, 54)( 36, 53)( 37, 52)( 38, 51)( 39, 50)( 40, 49)
( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 60, 87)( 61, 86)( 62, 85)( 63, 84)
( 64, 83)( 65, 82)( 66, 81)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 71, 76)
( 72, 75)( 73, 74)( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)( 94,111)
( 95,110)( 96,109)( 97,108)( 98,107)( 99,106)(100,105)(101,104)(102,103)
(118,145)(119,144)(120,143)(121,142)(122,141)(123,140)(124,139)(125,138)
(126,137)(127,136)(128,135)(129,134)(130,133)(131,132)(147,174)(148,173)
(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(155,166)(156,165)
(157,164)(158,163)(159,162)(160,161)(176,203)(177,202)(178,201)(179,200)
(180,199)(181,198)(182,197)(183,196)(184,195)(185,194)(186,193)(187,192)
(188,191)(189,190)(205,232)(206,231)(207,230)(208,229)(209,228)(210,227)
(211,226)(212,225)(213,224)(214,223)(215,222)(216,221)(217,220)(218,219);;
s1 := (  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, 89)( 60, 88)( 61,116)( 62,115)
( 63,114)( 64,113)( 65,112)( 66,111)( 67,110)( 68,109)( 69,108)( 70,107)
( 71,106)( 72,105)( 73,104)( 74,103)( 75,102)( 76,101)( 77,100)( 78, 99)
( 79, 98)( 80, 97)( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 85, 92)( 86, 91)
( 87, 90)(117,176)(118,175)(119,203)(120,202)(121,201)(122,200)(123,199)
(124,198)(125,197)(126,196)(127,195)(128,194)(129,193)(130,192)(131,191)
(132,190)(133,189)(134,188)(135,187)(136,186)(137,185)(138,184)(139,183)
(140,182)(141,181)(142,180)(143,179)(144,178)(145,177)(146,205)(147,204)
(148,232)(149,231)(150,230)(151,229)(152,228)(153,227)(154,226)(155,225)
(156,224)(157,223)(158,222)(159,221)(160,220)(161,219)(162,218)(163,217)
(164,216)(165,215)(166,214)(167,213)(168,212)(169,211)(170,210)(171,209)
(172,208)(173,207)(174,206);;
s2 := (  1,117)(  2,118)(  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)( 59,204)( 60,205)( 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)( 88,175)
( 89,176)( 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);;
s3 := (233,234);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope