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Polytope of Type {2,110,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,110,2,2}*1760
if this polytope has a name.
Group : SmallGroup(1760,1284)
Rank : 5
Schlafli Type : {2,110,2,2}
Number of vertices, edges, etc : 2, 110, 110, 2, 2
Order of s0s1s2s3s4 : 110
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 : {2,55,2,2}*880
5-fold quotients : {2,22,2,2}*352
10-fold quotients : {2,11,2,2}*176
11-fold quotients : {2,10,2,2}*160
22-fold quotients : {2,5,2,2}*80
55-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 14, 47)( 15, 57)( 16, 56)
( 17, 55)( 18, 54)( 19, 53)( 20, 52)( 21, 51)( 22, 50)( 23, 49)( 24, 48)
( 25, 36)( 26, 46)( 27, 45)( 28, 44)( 29, 43)( 30, 42)( 31, 41)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)
( 69,102)( 70,112)( 71,111)( 72,110)( 73,109)( 74,108)( 75,107)( 76,106)
( 77,105)( 78,104)( 79,103)( 80, 91)( 81,101)( 82,100)( 83, 99)( 84, 98)
( 85, 97)( 86, 96)( 87, 95)( 88, 94)( 89, 93)( 90, 92);;
s2 := ( 3, 70)( 4, 69)( 5, 79)( 6, 78)( 7, 77)( 8, 76)( 9, 75)( 10, 74)
( 11, 73)( 12, 72)( 13, 71)( 14, 59)( 15, 58)( 16, 68)( 17, 67)( 18, 66)
( 19, 65)( 20, 64)( 21, 63)( 22, 62)( 23, 61)( 24, 60)( 25,103)( 26,102)
( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)( 32,107)( 33,106)( 34,105)
( 35,104)( 36, 92)( 37, 91)( 38,101)( 39,100)( 40, 99)( 41, 98)( 42, 97)
( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 81)( 48, 80)( 49, 90)( 50, 89)
( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)( 57, 82);;
s3 := (113,114);;
s4 := (115,116);;
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*s1*s0*s1,
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(116)!(1,2);
s1 := Sym(116)!( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 14, 47)( 15, 57)
( 16, 56)( 17, 55)( 18, 54)( 19, 53)( 20, 52)( 21, 51)( 22, 50)( 23, 49)
( 24, 48)( 25, 36)( 26, 46)( 27, 45)( 28, 44)( 29, 43)( 30, 42)( 31, 41)
( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 59, 68)( 60, 67)( 61, 66)( 62, 65)
( 63, 64)( 69,102)( 70,112)( 71,111)( 72,110)( 73,109)( 74,108)( 75,107)
( 76,106)( 77,105)( 78,104)( 79,103)( 80, 91)( 81,101)( 82,100)( 83, 99)
( 84, 98)( 85, 97)( 86, 96)( 87, 95)( 88, 94)( 89, 93)( 90, 92);
s2 := Sym(116)!( 3, 70)( 4, 69)( 5, 79)( 6, 78)( 7, 77)( 8, 76)( 9, 75)
( 10, 74)( 11, 73)( 12, 72)( 13, 71)( 14, 59)( 15, 58)( 16, 68)( 17, 67)
( 18, 66)( 19, 65)( 20, 64)( 21, 63)( 22, 62)( 23, 61)( 24, 60)( 25,103)
( 26,102)( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)( 32,107)( 33,106)
( 34,105)( 35,104)( 36, 92)( 37, 91)( 38,101)( 39,100)( 40, 99)( 41, 98)
( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 81)( 48, 80)( 49, 90)
( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)( 57, 82);
s3 := Sym(116)!(113,114);
s4 := Sym(116)!(115,116);
poly := sub<Sym(116)|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*s1*s0*s1, 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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