Polytope of Type {2,2,2,10,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,10,10}*1600c
if this polytope has a name.
Group : SmallGroup(1600,10278)
Rank : 6
Schlafli Type : {2,2,2,10,10}
Number of vertices, edges, etc : 2, 2, 2, 10, 50, 10
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) :
2-fold quotients : {2,2,2,5,10}*800
5-fold quotients : {2,2,2,10,2}*320
10-fold quotients : {2,2,2,5,2}*160
25-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 7, 57)( 8, 61)( 9, 60)( 10, 59)( 11, 58)( 12, 77)( 13, 81)( 14, 80)
( 15, 79)( 16, 78)( 17, 72)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 67)
( 23, 71)( 24, 70)( 25, 69)( 26, 68)( 27, 62)( 28, 66)( 29, 65)( 30, 64)
( 31, 63)( 32, 82)( 33, 86)( 34, 85)( 35, 84)( 36, 83)( 37,102)( 38,106)
( 39,105)( 40,104)( 41,103)( 42, 97)( 43,101)( 44,100)( 45, 99)( 46, 98)
( 47, 92)( 48, 96)( 49, 95)( 50, 94)( 51, 93)( 52, 87)( 53, 91)( 54, 90)
( 55, 89)( 56, 88);;
s4 := ( 7, 88)( 8, 87)( 9, 91)( 10, 90)( 11, 89)( 12, 83)( 13, 82)( 14, 86)
( 15, 85)( 16, 84)( 17,103)( 18,102)( 19,106)( 20,105)( 21,104)( 22, 98)
( 23, 97)( 24,101)( 25,100)( 26, 99)( 27, 93)( 28, 92)( 29, 96)( 30, 95)
( 31, 94)( 32, 63)( 33, 62)( 34, 66)( 35, 65)( 36, 64)( 37, 58)( 38, 57)
( 39, 61)( 40, 60)( 41, 59)( 42, 78)( 43, 77)( 44, 81)( 45, 80)( 46, 79)
( 47, 73)( 48, 72)( 49, 76)( 50, 75)( 51, 74)( 52, 68)( 53, 67)( 54, 71)
( 55, 70)( 56, 69);;
s5 := ( 8, 11)( 9, 10)( 13, 16)( 14, 15)( 18, 21)( 19, 20)( 23, 26)( 24, 25)
( 28, 31)( 29, 30)( 33, 36)( 34, 35)( 38, 41)( 39, 40)( 43, 46)( 44, 45)
( 48, 51)( 49, 50)( 53, 56)( 54, 55)( 58, 61)( 59, 60)( 63, 66)( 64, 65)
( 68, 71)( 69, 70)( 73, 76)( 74, 75)( 78, 81)( 79, 80)( 83, 86)( 84, 85)
( 88, 91)( 89, 90)( 93, 96)( 94, 95)( 98,101)( 99,100)(103,106)(104,105);;
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s5*s4*s3*s4*s3*s4*s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(106)!(1,2);
s1 := Sym(106)!(3,4);
s2 := Sym(106)!(5,6);
s3 := Sym(106)!( 7, 57)( 8, 61)( 9, 60)( 10, 59)( 11, 58)( 12, 77)( 13, 81)
( 14, 80)( 15, 79)( 16, 78)( 17, 72)( 18, 76)( 19, 75)( 20, 74)( 21, 73)
( 22, 67)( 23, 71)( 24, 70)( 25, 69)( 26, 68)( 27, 62)( 28, 66)( 29, 65)
( 30, 64)( 31, 63)( 32, 82)( 33, 86)( 34, 85)( 35, 84)( 36, 83)( 37,102)
( 38,106)( 39,105)( 40,104)( 41,103)( 42, 97)( 43,101)( 44,100)( 45, 99)
( 46, 98)( 47, 92)( 48, 96)( 49, 95)( 50, 94)( 51, 93)( 52, 87)( 53, 91)
( 54, 90)( 55, 89)( 56, 88);
s4 := Sym(106)!( 7, 88)( 8, 87)( 9, 91)( 10, 90)( 11, 89)( 12, 83)( 13, 82)
( 14, 86)( 15, 85)( 16, 84)( 17,103)( 18,102)( 19,106)( 20,105)( 21,104)
( 22, 98)( 23, 97)( 24,101)( 25,100)( 26, 99)( 27, 93)( 28, 92)( 29, 96)
( 30, 95)( 31, 94)( 32, 63)( 33, 62)( 34, 66)( 35, 65)( 36, 64)( 37, 58)
( 38, 57)( 39, 61)( 40, 60)( 41, 59)( 42, 78)( 43, 77)( 44, 81)( 45, 80)
( 46, 79)( 47, 73)( 48, 72)( 49, 76)( 50, 75)( 51, 74)( 52, 68)( 53, 67)
( 54, 71)( 55, 70)( 56, 69);
s5 := Sym(106)!( 8, 11)( 9, 10)( 13, 16)( 14, 15)( 18, 21)( 19, 20)( 23, 26)
( 24, 25)( 28, 31)( 29, 30)( 33, 36)( 34, 35)( 38, 41)( 39, 40)( 43, 46)
( 44, 45)( 48, 51)( 49, 50)( 53, 56)( 54, 55)( 58, 61)( 59, 60)( 63, 66)
( 64, 65)( 68, 71)( 69, 70)( 73, 76)( 74, 75)( 78, 81)( 79, 80)( 83, 86)
( 84, 85)( 88, 91)( 89, 90)( 93, 96)( 94, 95)( 98,101)( 99,100)(103,106)
(104,105);
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*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s5*s4*s3*s4*s3*s4*s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope