Polytope of Type {30,15}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,15}*1200
if this polytope has a name.
Group : SmallGroup(1200,983)
Rank : 3
Schlafli Type : {30,15}
Number of vertices, edges, etc : 40, 300, 20
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 30
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {6,15}*240
   12-fold quotients : {10,5}*100
   25-fold quotients : {6,3}*48
   50-fold quotients : {3,3}*24
   60-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {30,15}

Twisty Puzzle