Polytope of Type {15,20}

Play with this polytope as a twisty puzzle

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

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {15,20}

Twisty Puzzle