Polytope of Type {4,58,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,58,2,2}*1856
if this polytope has a name.
Group : SmallGroup(1856,1369)
Rank : 5
Schlafli Type : {4,58,2,2}
Number of vertices, edges, etc : 4, 116, 58, 2, 2
Order of s0s1s2s3s4 : 116
Order of s0s1s2s3s4s3s2s1 : 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 : {2,58,2,2}*928
4-fold quotients : {2,29,2,2}*464
29-fold quotients : {4,2,2,2}*64
58-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 59, 88)( 60, 89)( 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);;
s1 := ( 1, 59)( 2, 87)( 3, 86)( 4, 85)( 5, 84)( 6, 83)( 7, 82)( 8, 81)
( 9, 80)( 10, 79)( 11, 78)( 12, 77)( 13, 76)( 14, 75)( 15, 74)( 16, 73)
( 17, 72)( 18, 71)( 19, 70)( 20, 69)( 21, 68)( 22, 67)( 23, 66)( 24, 65)
( 25, 64)( 26, 63)( 27, 62)( 28, 61)( 29, 60)( 30, 88)( 31,116)( 32,115)
( 33,114)( 34,113)( 35,112)( 36,111)( 37,110)( 38,109)( 39,108)( 40,107)
( 41,106)( 42,105)( 43,104)( 44,103)( 45,102)( 46,101)( 47,100)( 48, 99)
( 49, 98)( 50, 97)( 51, 96)( 52, 95)( 53, 94)( 54, 93)( 55, 92)( 56, 91)
( 57, 90)( 58, 89);;
s2 := ( 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, 60)( 61, 87)( 62, 86)( 63, 85)
( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)
( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)( 94,112)
( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)(102,104);;
s3 := (117,118);;
s4 := (119,120);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(120)!( 59, 88)( 60, 89)( 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);
s1 := Sym(120)!( 1, 59)( 2, 87)( 3, 86)( 4, 85)( 5, 84)( 6, 83)( 7, 82)
( 8, 81)( 9, 80)( 10, 79)( 11, 78)( 12, 77)( 13, 76)( 14, 75)( 15, 74)
( 16, 73)( 17, 72)( 18, 71)( 19, 70)( 20, 69)( 21, 68)( 22, 67)( 23, 66)
( 24, 65)( 25, 64)( 26, 63)( 27, 62)( 28, 61)( 29, 60)( 30, 88)( 31,116)
( 32,115)( 33,114)( 34,113)( 35,112)( 36,111)( 37,110)( 38,109)( 39,108)
( 40,107)( 41,106)( 42,105)( 43,104)( 44,103)( 45,102)( 46,101)( 47,100)
( 48, 99)( 49, 98)( 50, 97)( 51, 96)( 52, 95)( 53, 94)( 54, 93)( 55, 92)
( 56, 91)( 57, 90)( 58, 89);
s2 := Sym(120)!( 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, 60)( 61, 87)( 62, 86)
( 63, 85)( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)
( 71, 77)( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)
( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)
(102,104);
s3 := Sym(120)!(117,118);
s4 := Sym(120)!(119,120);
poly := sub<Sym(120)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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