Polytope of Type {2,2,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,12}*768b
if this polytope has a name.
Group : SmallGroup(768,1090143)
Rank : 5
Schlafli Type : {2,2,4,12}
Number of vertices, edges, etc : 2, 2, 8, 48, 24
Order of s₀s₁s₂s₃s₄ : 12
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 : {2,2,4,12}*384b, {2,2,4,12}*384c, {2,2,4,6}*384
   4-fold quotients : {2,2,2,12}*192, {2,2,4,3}*192, {2,2,4,6}*192b, {2,2,4,6}*192c
   8-fold quotients : {2,2,4,3}*96, {2,2,2,6}*96
   12-fold quotients : {2,2,2,4}*64
   16-fold quotients : {2,2,2,3}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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