Polytope of Type {10,10,2,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10,2,2,2}*1600a
if this polytope has a name.
Group : SmallGroup(1600,10278)
Rank : 6
Schlafli Type : {10,10,2,2,2}
Number of vertices, edges, etc : 10, 50, 10, 2, 2, 2
Order of s0s1s2s3s4s5 : 10
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,10,2,2,2}*320, {10,2,2,2,2}*320
10-fold quotients : {2,5,2,2,2}*160, {5,2,2,2,2}*160
25-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99);;
s1 := ( 1, 52)( 2, 51)( 3, 55)( 4, 54)( 5, 53)( 6, 72)( 7, 71)( 8, 75)
( 9, 74)( 10, 73)( 11, 67)( 12, 66)( 13, 70)( 14, 69)( 15, 68)( 16, 62)
( 17, 61)( 18, 65)( 19, 64)( 20, 63)( 21, 57)( 22, 56)( 23, 60)( 24, 59)
( 25, 58)( 26, 77)( 27, 76)( 28, 80)( 29, 79)( 30, 78)( 31, 97)( 32, 96)
( 33,100)( 34, 99)( 35, 98)( 36, 92)( 37, 91)( 38, 95)( 39, 94)( 40, 93)
( 41, 87)( 42, 86)( 43, 90)( 44, 89)( 45, 88)( 46, 82)( 47, 81)( 48, 85)
( 49, 84)( 50, 83);;
s2 := ( 1, 81)( 2, 82)( 3, 83)( 4, 84)( 5, 85)( 6, 76)( 7, 77)( 8, 78)
( 9, 79)( 10, 80)( 11, 96)( 12, 97)( 13, 98)( 14, 99)( 15,100)( 16, 91)
( 17, 92)( 18, 93)( 19, 94)( 20, 95)( 21, 86)( 22, 87)( 23, 88)( 24, 89)
( 25, 90)( 26, 56)( 27, 57)( 28, 58)( 29, 59)( 30, 60)( 31, 51)( 32, 52)
( 33, 53)( 34, 54)( 35, 55)( 36, 71)( 37, 72)( 38, 73)( 39, 74)( 40, 75)
( 41, 66)( 42, 67)( 43, 68)( 44, 69)( 45, 70)( 46, 61)( 47, 62)( 48, 63)
( 49, 64)( 50, 65);;
s3 := (101,102);;
s4 := (103,104);;
s5 := (105,106);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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(106)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)
( 98, 99);
s1 := Sym(106)!( 1, 52)( 2, 51)( 3, 55)( 4, 54)( 5, 53)( 6, 72)( 7, 71)
( 8, 75)( 9, 74)( 10, 73)( 11, 67)( 12, 66)( 13, 70)( 14, 69)( 15, 68)
( 16, 62)( 17, 61)( 18, 65)( 19, 64)( 20, 63)( 21, 57)( 22, 56)( 23, 60)
( 24, 59)( 25, 58)( 26, 77)( 27, 76)( 28, 80)( 29, 79)( 30, 78)( 31, 97)
( 32, 96)( 33,100)( 34, 99)( 35, 98)( 36, 92)( 37, 91)( 38, 95)( 39, 94)
( 40, 93)( 41, 87)( 42, 86)( 43, 90)( 44, 89)( 45, 88)( 46, 82)( 47, 81)
( 48, 85)( 49, 84)( 50, 83);
s2 := Sym(106)!( 1, 81)( 2, 82)( 3, 83)( 4, 84)( 5, 85)( 6, 76)( 7, 77)
( 8, 78)( 9, 79)( 10, 80)( 11, 96)( 12, 97)( 13, 98)( 14, 99)( 15,100)
( 16, 91)( 17, 92)( 18, 93)( 19, 94)( 20, 95)( 21, 86)( 22, 87)( 23, 88)
( 24, 89)( 25, 90)( 26, 56)( 27, 57)( 28, 58)( 29, 59)( 30, 60)( 31, 51)
( 32, 52)( 33, 53)( 34, 54)( 35, 55)( 36, 71)( 37, 72)( 38, 73)( 39, 74)
( 40, 75)( 41, 66)( 42, 67)( 43, 68)( 44, 69)( 45, 70)( 46, 61)( 47, 62)
( 48, 63)( 49, 64)( 50, 65);
s3 := Sym(106)!(101,102);
s4 := Sym(106)!(103,104);
s5 := Sym(106)!(105,106);
poly := sub<Sym(106)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope