Polytope of Type {5,2,8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,8,12}*1920a
if this polytope has a name.
Group : SmallGroup(1920,148891)
Rank : 5
Schlafli Type : {5,2,8,12}
Number of vertices, edges, etc : 5, 5, 8, 48, 12
Order of s₀s₁s₂s₃s₄ : 120
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 : {5,2,4,12}*960a, {5,2,8,6}*960
   3-fold quotients : {5,2,8,4}*640a
   4-fold quotients : {5,2,2,12}*480, {5,2,4,6}*480a
   6-fold quotients : {5,2,4,4}*320, {5,2,8,2}*320
   8-fold quotients : {5,2,2,6}*240
   12-fold quotients : {5,2,2,4}*160, {5,2,4,2}*160
   16-fold quotients : {5,2,2,3}*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 := (  6, 54)(  7, 55)(  8, 56)(  9, 57)( 10, 58)( 11, 59)( 12, 63)( 13, 64)
( 14, 65)( 15, 60)( 16, 61)( 17, 62)( 18, 66)( 19, 67)( 20, 68)( 21, 69)
( 22, 70)( 23, 71)( 24, 75)( 25, 76)( 26, 77)( 27, 72)( 28, 73)( 29, 74)
( 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, 39)( 13, 41)
( 14, 40)( 15, 36)( 16, 38)( 17, 37)( 18, 42)( 19, 44)( 20, 43)( 21, 45)
( 22, 47)( 23, 46)( 24, 51)( 25, 53)( 26, 52)( 27, 48)( 28, 50)( 29, 49)
( 54, 78)( 55, 80)( 56, 79)( 57, 81)( 58, 83)( 59, 82)( 60, 87)( 61, 89)
( 62, 88)( 63, 84)( 64, 86)( 65, 85)( 66, 90)( 67, 92)( 68, 91)( 69, 93)
( 70, 95)( 71, 94)( 72, 99)( 73,101)( 74,100)( 75, 96)( 76, 98)( 77, 97);;
s4 := (  6,  7)(  9, 10)( 12, 13)( 15, 16)( 18, 19)( 21, 22)( 24, 25)( 27, 28)
( 30, 43)( 31, 42)( 32, 44)( 33, 46)( 34, 45)( 35, 47)( 36, 49)( 37, 48)
( 38, 50)( 39, 52)( 40, 51)( 41, 53)( 54, 55)( 57, 58)( 60, 61)( 63, 64)
( 66, 67)( 69, 70)( 72, 73)( 75, 76)( 78, 91)( 79, 90)( 80, 92)( 81, 94)
( 82, 93)( 83, 95)( 84, 97)( 85, 96)( 86, 98)( 87,100)( 88, 99)( 89,101);;
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, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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, 63)
( 13, 64)( 14, 65)( 15, 60)( 16, 61)( 17, 62)( 18, 66)( 19, 67)( 20, 68)
( 21, 69)( 22, 70)( 23, 71)( 24, 75)( 25, 76)( 26, 77)( 27, 72)( 28, 73)
( 29, 74)( 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, 39)
( 13, 41)( 14, 40)( 15, 36)( 16, 38)( 17, 37)( 18, 42)( 19, 44)( 20, 43)
( 21, 45)( 22, 47)( 23, 46)( 24, 51)( 25, 53)( 26, 52)( 27, 48)( 28, 50)
( 29, 49)( 54, 78)( 55, 80)( 56, 79)( 57, 81)( 58, 83)( 59, 82)( 60, 87)
( 61, 89)( 62, 88)( 63, 84)( 64, 86)( 65, 85)( 66, 90)( 67, 92)( 68, 91)
( 69, 93)( 70, 95)( 71, 94)( 72, 99)( 73,101)( 74,100)( 75, 96)( 76, 98)
( 77, 97);
s4 := Sym(101)!(  6,  7)(  9, 10)( 12, 13)( 15, 16)( 18, 19)( 21, 22)( 24, 25)
( 27, 28)( 30, 43)( 31, 42)( 32, 44)( 33, 46)( 34, 45)( 35, 47)( 36, 49)
( 37, 48)( 38, 50)( 39, 52)( 40, 51)( 41, 53)( 54, 55)( 57, 58)( 60, 61)
( 63, 64)( 66, 67)( 69, 70)( 72, 73)( 75, 76)( 78, 91)( 79, 90)( 80, 92)
( 81, 94)( 82, 93)( 83, 95)( 84, 97)( 85, 96)( 86, 98)( 87,100)( 88, 99)
( 89,101);
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, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope