Polytope of Type {2,10,22,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,22,2}*1760
if this polytope has a name.
Group : SmallGroup(1760,1281)
Rank : 5
Schlafli Type : {2,10,22,2}
Number of vertices, edges, etc : 2, 10, 110, 22, 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) :
5-fold quotients : {2,2,22,2}*352
10-fold quotients : {2,2,11,2}*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 := ( 14, 47)( 15, 48)( 16, 49)( 17, 50)( 18, 51)( 19, 52)( 20, 53)( 21, 54)
( 22, 55)( 23, 56)( 24, 57)( 25, 36)( 26, 37)( 27, 38)( 28, 39)( 29, 40)
( 30, 41)( 31, 42)( 32, 43)( 33, 44)( 34, 45)( 35, 46)( 69,102)( 70,103)
( 71,104)( 72,105)( 73,106)( 74,107)( 75,108)( 76,109)( 77,110)( 78,111)
( 79,112)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)( 86, 97)
( 87, 98)( 88, 99)( 89,100)( 90,101);;
s2 := ( 3, 14)( 4, 24)( 5, 23)( 6, 22)( 7, 21)( 8, 20)( 9, 19)( 10, 18)
( 11, 17)( 12, 16)( 13, 15)( 25, 47)( 26, 57)( 27, 56)( 28, 55)( 29, 54)
( 30, 53)( 31, 52)( 32, 51)( 33, 50)( 34, 49)( 35, 48)( 37, 46)( 38, 45)
( 39, 44)( 40, 43)( 41, 42)( 58, 69)( 59, 79)( 60, 78)( 61, 77)( 62, 76)
( 63, 75)( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70)( 80,102)( 81,112)
( 82,111)( 83,110)( 84,109)( 85,108)( 86,107)( 87,106)( 88,105)( 89,104)
( 90,103)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97);;
s3 := ( 3, 59)( 4, 58)( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 64)( 10, 63)
( 11, 62)( 12, 61)( 13, 60)( 14, 70)( 15, 69)( 16, 79)( 17, 78)( 18, 77)
( 19, 76)( 20, 75)( 21, 74)( 22, 73)( 23, 72)( 24, 71)( 25, 81)( 26, 80)
( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 86)( 32, 85)( 33, 84)( 34, 83)
( 35, 82)( 36, 92)( 37, 91)( 38,101)( 39,100)( 40, 99)( 41, 98)( 42, 97)
( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47,103)( 48,102)( 49,112)( 50,111)
( 51,110)( 52,109)( 53,108)( 54,107)( 55,106)( 56,105)( 57,104);;
s4 := (113,114);;
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,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(114)!(1,2);
s1 := Sym(114)!( 14, 47)( 15, 48)( 16, 49)( 17, 50)( 18, 51)( 19, 52)( 20, 53)
( 21, 54)( 22, 55)( 23, 56)( 24, 57)( 25, 36)( 26, 37)( 27, 38)( 28, 39)
( 29, 40)( 30, 41)( 31, 42)( 32, 43)( 33, 44)( 34, 45)( 35, 46)( 69,102)
( 70,103)( 71,104)( 72,105)( 73,106)( 74,107)( 75,108)( 76,109)( 77,110)
( 78,111)( 79,112)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)
( 86, 97)( 87, 98)( 88, 99)( 89,100)( 90,101);
s2 := Sym(114)!( 3, 14)( 4, 24)( 5, 23)( 6, 22)( 7, 21)( 8, 20)( 9, 19)
( 10, 18)( 11, 17)( 12, 16)( 13, 15)( 25, 47)( 26, 57)( 27, 56)( 28, 55)
( 29, 54)( 30, 53)( 31, 52)( 32, 51)( 33, 50)( 34, 49)( 35, 48)( 37, 46)
( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 58, 69)( 59, 79)( 60, 78)( 61, 77)
( 62, 76)( 63, 75)( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70)( 80,102)
( 81,112)( 82,111)( 83,110)( 84,109)( 85,108)( 86,107)( 87,106)( 88,105)
( 89,104)( 90,103)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97);
s3 := Sym(114)!( 3, 59)( 4, 58)( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 64)
( 10, 63)( 11, 62)( 12, 61)( 13, 60)( 14, 70)( 15, 69)( 16, 79)( 17, 78)
( 18, 77)( 19, 76)( 20, 75)( 21, 74)( 22, 73)( 23, 72)( 24, 71)( 25, 81)
( 26, 80)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 86)( 32, 85)( 33, 84)
( 34, 83)( 35, 82)( 36, 92)( 37, 91)( 38,101)( 39,100)( 40, 99)( 41, 98)
( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47,103)( 48,102)( 49,112)
( 50,111)( 51,110)( 52,109)( 53,108)( 54,107)( 55,106)( 56,105)( 57,104);
s4 := Sym(114)!(113,114);
poly := sub<Sym(114)|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, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope