Polytope of Type {2,58,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,58,6}*1392
if this polytope has a name.
Group : SmallGroup(1392,192)
Rank : 4
Schlafli Type : {2,58,6}
Number of vertices, edges, etc : 2, 58, 174, 6
Order of s₀s₁s₂s₃ : 174
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) :
   3-fold quotients : {2,58,2}*464
   6-fold quotients : {2,29,2}*232
   29-fold quotients : {2,2,6}*48
   58-fold quotients : {2,2,3}*24
   87-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);;
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, 62)( 33, 61)
( 34, 89)( 35, 88)( 36, 87)( 37, 86)( 38, 85)( 39, 84)( 40, 83)( 41, 82)
( 42, 81)( 43, 80)( 44, 79)( 45, 78)( 46, 77)( 47, 76)( 48, 75)( 49, 74)
( 50, 73)( 51, 72)( 52, 71)( 53, 70)( 54, 69)( 55, 68)( 56, 67)( 57, 66)
( 58, 65)( 59, 64)( 60, 63)( 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)(119,149)(120,148)(121,176)(122,175)(123,174)(124,173)(125,172)
(126,171)(127,170)(128,169)(129,168)(130,167)(131,166)(132,165)(133,164)
(134,163)(135,162)(136,161)(137,160)(138,159)(139,158)(140,157)(141,156)
(142,155)(143,154)(144,153)(145,152)(146,151)(147,150);;
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, 90)( 33, 91)( 34, 92)
( 35, 93)( 36, 94)( 37, 95)( 38, 96)( 39, 97)( 40, 98)( 41, 99)( 42,100)
( 43,101)( 44,102)( 45,103)( 46,104)( 47,105)( 48,106)( 49,107)( 50,108)
( 51,109)( 52,110)( 53,111)( 54,112)( 55,113)( 56,114)( 57,115)( 58,116)
( 59,117)( 60,118)( 61,148)( 62,149)( 63,150)( 64,151)( 65,152)( 66,153)
( 67,154)( 68,155)( 69,156)( 70,157)( 71,158)( 72,159)( 73,160)( 74,161)
( 75,162)( 76,163)( 77,164)( 78,165)( 79,166)( 80,167)( 81,168)( 82,169)
( 83,170)( 84,171)( 85,172)( 86,173)( 87,174)( 88,175)( 89,176);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(176)!(1,2);
s1 := Sym(176)!(  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);
s2 := Sym(176)!(  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, 62)
( 33, 61)( 34, 89)( 35, 88)( 36, 87)( 37, 86)( 38, 85)( 39, 84)( 40, 83)
( 41, 82)( 42, 81)( 43, 80)( 44, 79)( 45, 78)( 46, 77)( 47, 76)( 48, 75)
( 49, 74)( 50, 73)( 51, 72)( 52, 71)( 53, 70)( 54, 69)( 55, 68)( 56, 67)
( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 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)(119,149)(120,148)(121,176)(122,175)(123,174)(124,173)
(125,172)(126,171)(127,170)(128,169)(129,168)(130,167)(131,166)(132,165)
(133,164)(134,163)(135,162)(136,161)(137,160)(138,159)(139,158)(140,157)
(141,156)(142,155)(143,154)(144,153)(145,152)(146,151)(147,150);
s3 := Sym(176)!(  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, 90)( 33, 91)
( 34, 92)( 35, 93)( 36, 94)( 37, 95)( 38, 96)( 39, 97)( 40, 98)( 41, 99)
( 42,100)( 43,101)( 44,102)( 45,103)( 46,104)( 47,105)( 48,106)( 49,107)
( 50,108)( 51,109)( 52,110)( 53,111)( 54,112)( 55,113)( 56,114)( 57,115)
( 58,116)( 59,117)( 60,118)( 61,148)( 62,149)( 63,150)( 64,151)( 65,152)
( 66,153)( 67,154)( 68,155)( 69,156)( 70,157)( 71,158)( 72,159)( 73,160)
( 74,161)( 75,162)( 76,163)( 77,164)( 78,165)( 79,166)( 80,167)( 81,168)
( 82,169)( 83,170)( 84,171)( 85,172)( 86,173)( 87,174)( 88,175)( 89,176);
poly := sub<Sym(176)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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