Polytope of Type {2,58,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,58,4}*928
if this polytope has a name.
Group : SmallGroup(928,216)
Rank : 4
Schlafli Type : {2,58,4}
Number of vertices, edges, etc : 2, 58, 116, 4
Order of s₀s₁s₂s₃ : 116
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,58,4,2} of size 1856
Vertex Figure Of :
   {2,2,58,4} of size 1856
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,58,2}*464
   4-fold quotients : {2,29,2}*232
   29-fold quotients : {2,2,4}*32
   58-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,116,4}*1856, {4,58,4}*1856, {2,58,8}*1856
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);;
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);;
s3 := (  3, 61)(  4, 62)(  5, 63)(  6, 64)(  7, 65)(  8, 66)(  9, 67)( 10, 68)
( 11, 69)( 12, 70)( 13, 71)( 14, 72)( 15, 73)( 16, 74)( 17, 75)( 18, 76)
( 19, 77)( 20, 78)( 21, 79)( 22, 80)( 23, 81)( 24, 82)( 25, 83)( 26, 84)
( 27, 85)( 28, 86)( 29, 87)( 30, 88)( 31, 89)( 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);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(118)!(1,2);
s1 := Sym(118)!(  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);
s2 := Sym(118)!(  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);
s3 := Sym(118)!(  3, 61)(  4, 62)(  5, 63)(  6, 64)(  7, 65)(  8, 66)(  9, 67)
( 10, 68)( 11, 69)( 12, 70)( 13, 71)( 14, 72)( 15, 73)( 16, 74)( 17, 75)
( 18, 76)( 19, 77)( 20, 78)( 21, 79)( 22, 80)( 23, 81)( 24, 82)( 25, 83)
( 26, 84)( 27, 85)( 28, 86)( 29, 87)( 30, 88)( 31, 89)( 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);
poly := sub<Sym(118)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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