Polytope of Type {20,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,30}*1200d
if this polytope has a name.
Group : SmallGroup(1200,983)
Rank : 3
Schlafli Type : {20,30}
Number of vertices, edges, etc : 20, 300, 30
Order of s₀s₁s₂ : 15
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {20,6}*240b, {4,30}*240c
   10-fold quotients : {4,15}*120
   25-fold quotients : {4,6}*48b
   50-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope