Polytope of Type {5,2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,6,8}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240195)
Rank : 5
Schlafli Type : {5,2,6,8}
Number of vertices, edges, etc : 5, 5, 12, 48, 16
Order of s₀s₁s₂s₃s₄ : 60
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) :
   2-fold quotients : {5,2,3,8}*960, {5,2,6,4}*960
   4-fold quotients : {5,2,3,4}*480, {5,2,6,4}*480b, {5,2,6,4}*480c
   8-fold quotients : {5,2,3,4}*240, {5,2,6,2}*240
   16-fold quotients : {5,2,3,2}*120
   24-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope