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}*1600b
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 : {2,2,2,10,5}*800
5-fold quotients : {2,2,2,2,10}*320
10-fold quotients : {2,2,2,2,5}*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 := ( 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);;
s4 := ( 7, 58)( 8, 57)( 9, 61)( 10, 60)( 11, 59)( 12, 78)( 13, 77)( 14, 81)
( 15, 80)( 16, 79)( 17, 73)( 18, 72)( 19, 76)( 20, 75)( 21, 74)( 22, 68)
( 23, 67)( 24, 71)( 25, 70)( 26, 69)( 27, 63)( 28, 62)( 29, 66)( 30, 65)
( 31, 64)( 32, 83)( 33, 82)( 34, 86)( 35, 85)( 36, 84)( 37,103)( 38,102)
( 39,106)( 40,105)( 41,104)( 42, 98)( 43, 97)( 44,101)( 45,100)( 46, 99)
( 47, 93)( 48, 92)( 49, 96)( 50, 95)( 51, 94)( 52, 88)( 53, 87)( 54, 91)
( 55, 90)( 56, 89);;
s5 := ( 7, 87)( 8, 91)( 9, 90)( 10, 89)( 11, 88)( 12, 82)( 13, 86)( 14, 85)
( 15, 84)( 16, 83)( 17,102)( 18,106)( 19,105)( 20,104)( 21,103)( 22, 97)
( 23,101)( 24,100)( 25, 99)( 26, 98)( 27, 92)( 28, 96)( 29, 95)( 30, 94)
( 31, 93)( 32, 62)( 33, 66)( 34, 65)( 35, 64)( 36, 63)( 37, 57)( 38, 61)
( 39, 60)( 40, 59)( 41, 58)( 42, 77)( 43, 81)( 44, 80)( 45, 79)( 46, 78)
( 47, 72)( 48, 76)( 49, 75)( 50, 74)( 51, 73)( 52, 67)( 53, 71)( 54, 70)
( 55, 69)( 56, 68);;
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*s3*s4*s5*s3*s4*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(106)!(1,2);
s1 := Sym(106)!(3,4);
s2 := Sym(106)!(5,6);
s3 := 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);
s4 := Sym(106)!( 7, 58)( 8, 57)( 9, 61)( 10, 60)( 11, 59)( 12, 78)( 13, 77)
( 14, 81)( 15, 80)( 16, 79)( 17, 73)( 18, 72)( 19, 76)( 20, 75)( 21, 74)
( 22, 68)( 23, 67)( 24, 71)( 25, 70)( 26, 69)( 27, 63)( 28, 62)( 29, 66)
( 30, 65)( 31, 64)( 32, 83)( 33, 82)( 34, 86)( 35, 85)( 36, 84)( 37,103)
( 38,102)( 39,106)( 40,105)( 41,104)( 42, 98)( 43, 97)( 44,101)( 45,100)
( 46, 99)( 47, 93)( 48, 92)( 49, 96)( 50, 95)( 51, 94)( 52, 88)( 53, 87)
( 54, 91)( 55, 90)( 56, 89);
s5 := Sym(106)!( 7, 87)( 8, 91)( 9, 90)( 10, 89)( 11, 88)( 12, 82)( 13, 86)
( 14, 85)( 15, 84)( 16, 83)( 17,102)( 18,106)( 19,105)( 20,104)( 21,103)
( 22, 97)( 23,101)( 24,100)( 25, 99)( 26, 98)( 27, 92)( 28, 96)( 29, 95)
( 30, 94)( 31, 93)( 32, 62)( 33, 66)( 34, 65)( 35, 64)( 36, 63)( 37, 57)
( 38, 61)( 39, 60)( 40, 59)( 41, 58)( 42, 77)( 43, 81)( 44, 80)( 45, 79)
( 46, 78)( 47, 72)( 48, 76)( 49, 75)( 50, 74)( 51, 73)( 52, 67)( 53, 71)
( 54, 70)( 55, 69)( 56, 68);
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*s3*s4*s5*s3*s4*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;
to this polytope