Polytope of Type {5,2,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,12,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240195)
Rank : 5
Schlafli Type : {5,2,12,6}
Number of vertices, edges, etc : 5, 5, 16, 48, 8
Order of s₀s₁s₂s₃s₄ : 40
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 : {5,2,12,3}*960, {5,2,6,6}*960
   4-fold quotients : {5,2,3,6}*480, {5,2,6,3}*480
   8-fold quotients : {5,2,3,3}*240
   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, 38)(  7, 39)(  8, 41)(  9, 40)( 10, 44)( 11, 45)( 12, 42)( 13, 43)
( 14, 30)( 15, 31)( 16, 33)( 17, 32)( 18, 36)( 19, 37)( 20, 34)( 21, 35)
( 22, 46)( 23, 47)( 24, 49)( 25, 48)( 26, 52)( 27, 53)( 28, 50)( 29, 51)
( 54, 86)( 55, 87)( 56, 89)( 57, 88)( 58, 92)( 59, 93)( 60, 90)( 61, 91)
( 62, 78)( 63, 79)( 64, 81)( 65, 80)( 66, 84)( 67, 85)( 68, 82)( 69, 83)
( 70, 94)( 71, 95)( 72, 97)( 73, 96)( 74,100)( 75,101)( 76, 98)( 77, 99);;
s4 := (  6, 84)(  7, 85)(  8, 81)(  9, 80)( 10, 82)( 11, 83)( 12, 78)( 13, 79)
( 14,100)( 15,101)( 16, 97)( 17, 96)( 18, 98)( 19, 99)( 20, 94)( 21, 95)
( 22, 92)( 23, 93)( 24, 89)( 25, 88)( 26, 90)( 27, 91)( 28, 86)( 29, 87)
( 30, 60)( 31, 61)( 32, 57)( 33, 56)( 34, 58)( 35, 59)( 36, 54)( 37, 55)
( 38, 76)( 39, 77)( 40, 73)( 41, 72)( 42, 74)( 43, 75)( 44, 70)( 45, 71)
( 46, 68)( 47, 69)( 48, 65)( 49, 64)( 50, 66)( 51, 67)( 52, 62)( 53, 63);;
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*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s2*s3*s2*s3*s4*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)!(  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, 38)(  7, 39)(  8, 41)(  9, 40)( 10, 44)( 11, 45)( 12, 42)
( 13, 43)( 14, 30)( 15, 31)( 16, 33)( 17, 32)( 18, 36)( 19, 37)( 20, 34)
( 21, 35)( 22, 46)( 23, 47)( 24, 49)( 25, 48)( 26, 52)( 27, 53)( 28, 50)
( 29, 51)( 54, 86)( 55, 87)( 56, 89)( 57, 88)( 58, 92)( 59, 93)( 60, 90)
( 61, 91)( 62, 78)( 63, 79)( 64, 81)( 65, 80)( 66, 84)( 67, 85)( 68, 82)
( 69, 83)( 70, 94)( 71, 95)( 72, 97)( 73, 96)( 74,100)( 75,101)( 76, 98)
( 77, 99);
s4 := Sym(101)!(  6, 84)(  7, 85)(  8, 81)(  9, 80)( 10, 82)( 11, 83)( 12, 78)
( 13, 79)( 14,100)( 15,101)( 16, 97)( 17, 96)( 18, 98)( 19, 99)( 20, 94)
( 21, 95)( 22, 92)( 23, 93)( 24, 89)( 25, 88)( 26, 90)( 27, 91)( 28, 86)
( 29, 87)( 30, 60)( 31, 61)( 32, 57)( 33, 56)( 34, 58)( 35, 59)( 36, 54)
( 37, 55)( 38, 76)( 39, 77)( 40, 73)( 41, 72)( 42, 74)( 43, 75)( 44, 70)
( 45, 71)( 46, 68)( 47, 69)( 48, 65)( 49, 64)( 50, 66)( 51, 67)( 52, 62)
( 53, 63);
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*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3 >;

to this polytope