Polytope of Type {5,2,4,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,6,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,208116)
Rank : 6
Schlafli Type : {5,2,4,6,4}
Number of vertices, edges, etc : 5, 5, 4, 12, 12, 4
Order of s0s1s2s3s4s5 : 60
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 : {5,2,2,6,4}*960a, {5,2,4,6,2}*960a
3-fold quotients : {5,2,4,2,4}*640
4-fold quotients : {5,2,2,6,2}*480
6-fold quotients : {5,2,2,2,4}*320, {5,2,4,2,2}*320
8-fold quotients : {5,2,2,3,2}*240
12-fold quotients : {5,2,2,2,2}*160
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 61)
( 14, 62)( 15, 63)( 16, 64)( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 69)
( 22, 70)( 23, 71)( 24, 72)( 25, 73)( 26, 74)( 27, 75)( 28, 76)( 29, 77)
( 30, 84)( 31, 85)( 32, 86)( 33, 87)( 34, 88)( 35, 89)( 36, 78)( 37, 79)
( 38, 80)( 39, 81)( 40, 82)( 41, 83)( 42, 96)( 43, 97)( 44, 98)( 45, 99)
( 46,100)( 47,101)( 48, 90)( 49, 91)( 50, 92)( 51, 93)( 52, 94)( 53, 95);;
s3 := ( 6, 30)( 7, 32)( 8, 31)( 9, 33)( 10, 35)( 11, 34)( 12, 36)( 13, 38)
( 14, 37)( 15, 39)( 16, 41)( 17, 40)( 18, 48)( 19, 50)( 20, 49)( 21, 51)
( 22, 53)( 23, 52)( 24, 42)( 25, 44)( 26, 43)( 27, 45)( 28, 47)( 29, 46)
( 54, 78)( 55, 80)( 56, 79)( 57, 81)( 58, 83)( 59, 82)( 60, 84)( 61, 86)
( 62, 85)( 63, 87)( 64, 89)( 65, 88)( 66, 96)( 67, 98)( 68, 97)( 69, 99)
( 70,101)( 71,100)( 72, 90)( 73, 92)( 74, 91)( 75, 93)( 76, 95)( 77, 94);;
s4 := ( 6, 7)( 9, 10)( 12, 13)( 15, 16)( 18, 28)( 19, 27)( 20, 29)( 21, 25)
( 22, 24)( 23, 26)( 30, 31)( 33, 34)( 36, 37)( 39, 40)( 42, 52)( 43, 51)
( 44, 53)( 45, 49)( 46, 48)( 47, 50)( 54, 55)( 57, 58)( 60, 61)( 63, 64)
( 66, 76)( 67, 75)( 68, 77)( 69, 73)( 70, 72)( 71, 74)( 78, 79)( 81, 82)
( 84, 85)( 87, 88)( 90,100)( 91, 99)( 92,101)( 93, 97)( 94, 96)( 95, 98);;
s5 := ( 6, 66)( 7, 67)( 8, 68)( 9, 69)( 10, 70)( 11, 71)( 12, 72)( 13, 73)
( 14, 74)( 15, 75)( 16, 76)( 17, 77)( 18, 54)( 19, 55)( 20, 56)( 21, 57)
( 22, 58)( 23, 59)( 24, 60)( 25, 61)( 26, 62)( 27, 63)( 28, 64)( 29, 65)
( 30, 96)( 31, 97)( 32, 98)( 33, 99)( 34,100)( 35,101)( 36, 90)( 37, 91)
( 38, 92)( 39, 93)( 40, 94)( 41, 95)( 42, 84)( 43, 85)( 44, 86)( 45, 87)
( 46, 88)( 47, 89)( 48, 78)( 49, 79)( 50, 80)( 51, 81)( 52, 82)( 53, 83);;
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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*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, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(101)!(2,3)(4,5);
s1 := Sym(101)!(1,2)(3,4);
s2 := Sym(101)!( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)( 11, 59)( 12, 60)
( 13, 61)( 14, 62)( 15, 63)( 16, 64)( 17, 65)( 18, 66)( 19, 67)( 20, 68)
( 21, 69)( 22, 70)( 23, 71)( 24, 72)( 25, 73)( 26, 74)( 27, 75)( 28, 76)
( 29, 77)( 30, 84)( 31, 85)( 32, 86)( 33, 87)( 34, 88)( 35, 89)( 36, 78)
( 37, 79)( 38, 80)( 39, 81)( 40, 82)( 41, 83)( 42, 96)( 43, 97)( 44, 98)
( 45, 99)( 46,100)( 47,101)( 48, 90)( 49, 91)( 50, 92)( 51, 93)( 52, 94)
( 53, 95);
s3 := Sym(101)!( 6, 30)( 7, 32)( 8, 31)( 9, 33)( 10, 35)( 11, 34)( 12, 36)
( 13, 38)( 14, 37)( 15, 39)( 16, 41)( 17, 40)( 18, 48)( 19, 50)( 20, 49)
( 21, 51)( 22, 53)( 23, 52)( 24, 42)( 25, 44)( 26, 43)( 27, 45)( 28, 47)
( 29, 46)( 54, 78)( 55, 80)( 56, 79)( 57, 81)( 58, 83)( 59, 82)( 60, 84)
( 61, 86)( 62, 85)( 63, 87)( 64, 89)( 65, 88)( 66, 96)( 67, 98)( 68, 97)
( 69, 99)( 70,101)( 71,100)( 72, 90)( 73, 92)( 74, 91)( 75, 93)( 76, 95)
( 77, 94);
s4 := Sym(101)!( 6, 7)( 9, 10)( 12, 13)( 15, 16)( 18, 28)( 19, 27)( 20, 29)
( 21, 25)( 22, 24)( 23, 26)( 30, 31)( 33, 34)( 36, 37)( 39, 40)( 42, 52)
( 43, 51)( 44, 53)( 45, 49)( 46, 48)( 47, 50)( 54, 55)( 57, 58)( 60, 61)
( 63, 64)( 66, 76)( 67, 75)( 68, 77)( 69, 73)( 70, 72)( 71, 74)( 78, 79)
( 81, 82)( 84, 85)( 87, 88)( 90,100)( 91, 99)( 92,101)( 93, 97)( 94, 96)
( 95, 98);
s5 := Sym(101)!( 6, 66)( 7, 67)( 8, 68)( 9, 69)( 10, 70)( 11, 71)( 12, 72)
( 13, 73)( 14, 74)( 15, 75)( 16, 76)( 17, 77)( 18, 54)( 19, 55)( 20, 56)
( 21, 57)( 22, 58)( 23, 59)( 24, 60)( 25, 61)( 26, 62)( 27, 63)( 28, 64)
( 29, 65)( 30, 96)( 31, 97)( 32, 98)( 33, 99)( 34,100)( 35,101)( 36, 90)
( 37, 91)( 38, 92)( 39, 93)( 40, 94)( 41, 95)( 42, 84)( 43, 85)( 44, 86)
( 45, 87)( 46, 88)( 47, 89)( 48, 78)( 49, 79)( 50, 80)( 51, 81)( 52, 82)
( 53, 83);
poly := sub<Sym(101)|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, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*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,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope