Polytope of Type {5,2,4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,24}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150682)
Rank : 5
Schlafli Type : {5,2,4,24}
Number of vertices, edges, etc : 5, 5, 4, 48, 24
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
   3-fold quotients : {5,2,4,8}*640b
   4-fold quotients : {5,2,2,12}*480, {5,2,4,6}*480a
   6-fold quotients : {5,2,4,4}*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, 60)( 13, 61)
( 14, 62)( 15, 63)( 16, 64)( 17, 65)( 18, 69)( 19, 70)( 20, 71)( 21, 66)
( 22, 67)( 23, 68)( 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, 99)( 43,100)( 44,101)( 45, 96)
( 46, 97)( 47, 98)( 48, 93)( 49, 94)( 50, 95)( 51, 90)( 52, 91)( 53, 92);;
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, 45)( 19, 47)( 20, 46)( 21, 42)
( 22, 44)( 23, 43)( 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, 84)( 61, 86)
( 62, 85)( 63, 87)( 64, 89)( 65, 88)( 66, 93)( 67, 95)( 68, 94)( 69, 90)
( 70, 92)( 71, 91)( 72, 99)( 73,101)( 74,100)( 75, 96)( 76, 98)( 77, 97);;
s4 := (  6,  7)(  9, 10)( 12, 16)( 13, 15)( 14, 17)( 18, 22)( 19, 21)( 20, 23)
( 24, 25)( 27, 28)( 30, 43)( 31, 42)( 32, 44)( 33, 46)( 34, 45)( 35, 47)
( 36, 52)( 37, 51)( 38, 53)( 39, 49)( 40, 48)( 41, 50)( 54, 55)( 57, 58)
( 60, 64)( 61, 63)( 62, 65)( 66, 70)( 67, 69)( 68, 71)( 72, 73)( 75, 76)
( 78, 91)( 79, 90)( 80, 92)( 81, 94)( 82, 93)( 83, 95)( 84,100)( 85, 99)
( 86,101)( 87, 97)( 88, 96)( 89, 98);;
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*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3 ];;
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, 69)( 19, 70)( 20, 71)
( 21, 66)( 22, 67)( 23, 68)( 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, 99)( 43,100)( 44,101)
( 45, 96)( 46, 97)( 47, 98)( 48, 93)( 49, 94)( 50, 95)( 51, 90)( 52, 91)
( 53, 92);
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, 45)( 19, 47)( 20, 46)
( 21, 42)( 22, 44)( 23, 43)( 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, 84)
( 61, 86)( 62, 85)( 63, 87)( 64, 89)( 65, 88)( 66, 93)( 67, 95)( 68, 94)
( 69, 90)( 70, 92)( 71, 91)( 72, 99)( 73,101)( 74,100)( 75, 96)( 76, 98)
( 77, 97);
s4 := Sym(101)!(  6,  7)(  9, 10)( 12, 16)( 13, 15)( 14, 17)( 18, 22)( 19, 21)
( 20, 23)( 24, 25)( 27, 28)( 30, 43)( 31, 42)( 32, 44)( 33, 46)( 34, 45)
( 35, 47)( 36, 52)( 37, 51)( 38, 53)( 39, 49)( 40, 48)( 41, 50)( 54, 55)
( 57, 58)( 60, 64)( 61, 63)( 62, 65)( 66, 70)( 67, 69)( 68, 71)( 72, 73)
( 75, 76)( 78, 91)( 79, 90)( 80, 92)( 81, 94)( 82, 93)( 83, 95)( 84,100)
( 85, 99)( 86,101)( 87, 97)( 88, 96)( 89, 98);
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*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3 >;

to this polytope