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

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

to this polytope