Polytope of Type {20,15}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,15}*1200
if this polytope has a name.
Group : SmallGroup(1200,983)
Rank : 3
Schlafli Type : {20,15}
Number of vertices, edges, etc : 40, 300, 30
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 20
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) :
   4-fold quotients : {10,15}*300
   5-fold quotients : {4,15}*240
   10-fold quotients : {4,15}*120
   12-fold quotients : {10,5}*100
   20-fold quotients : {2,15}*60
   25-fold quotients : {4,3}*48
   50-fold quotients : {4,3}*24
   60-fold quotients : {2,5}*20
   100-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 2.
      20 facets:
         10 of {10}*20
         10 of {20}*40
      20 vertex figures:
         20 of {15}*30
   P/N, where N=<s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 2.
      15 facets:
         15 of {20}*40
      20 vertex figures:
         20 of {15}*30

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, 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);;
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*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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, 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);
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*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope

Polytope of Type {20,15}

Twisty Puzzle