Polytope of Type {6,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,15}*1500a
if this polytope has a name.
Group : SmallGroup(1500,37)
Rank : 3
Schlafli Type : {6,15}
Number of vertices, edges, etc : 50, 375, 125
Order of s₀s₁s₂ : 10
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 : {6,3}*300
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  5)(  3,  4)(  6, 35)(  7, 34)(  8, 33)(  9, 32)( 10, 31)( 11, 61)
( 12, 65)( 13, 64)( 14, 63)( 15, 62)( 16, 94)( 17, 93)( 18, 92)( 19, 91)
( 20, 95)( 21,124)( 22,123)( 23,122)( 24,121)( 25,125)( 26,101)( 27,105)
( 28,104)( 29,103)( 30,102)( 37, 40)( 38, 39)( 41, 69)( 42, 68)( 43, 67)
( 44, 66)( 45, 70)( 46, 99)( 47, 98)( 48, 97)( 49, 96)( 50,100)( 51, 76)
( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56,110)( 57,109)( 58,108)( 59,107)
( 60,106)( 71, 74)( 72, 73)( 81, 85)( 82, 84)( 86,111)( 87,115)( 88,114)
( 89,113)( 90,112)(116,119)(117,118);;
s1 := (  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26, 41)( 27, 45)( 28, 44)( 29, 43)
( 30, 42)( 31, 36)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 50)( 48, 49)
( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)( 63, 75)
( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 99)( 77, 98)( 78, 97)( 79, 96)
( 80,100)( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 85, 95)( 86, 89)( 87, 88)
(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)(116,122)
(117,121)(118,125)(119,124)(120,123);;
s2 := (  1, 36)(  2, 40)(  3, 39)(  4, 38)(  5, 37)(  6, 10)(  7,  9)( 11,101)
( 12,105)( 13,104)( 14,103)( 15,102)( 16, 99)( 17, 98)( 18, 97)( 19, 96)
( 20,100)( 21, 69)( 22, 68)( 23, 67)( 24, 66)( 25, 70)( 26, 61)( 27, 65)
( 28, 64)( 29, 63)( 30, 62)( 31, 35)( 32, 34)( 41,124)( 42,123)( 43,122)
( 44,121)( 45,125)( 46, 94)( 47, 93)( 48, 92)( 49, 91)( 50, 95)( 51, 86)
( 52, 90)( 53, 89)( 54, 88)( 55, 87)( 56, 60)( 57, 59)( 71,119)( 72,118)
( 73,117)( 74,116)( 75,120)( 76,111)( 77,115)( 78,114)( 79,113)( 80,112)
( 81, 85)( 82, 84)(106,110)(107,109);;
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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(125)!(  2,  5)(  3,  4)(  6, 35)(  7, 34)(  8, 33)(  9, 32)( 10, 31)
( 11, 61)( 12, 65)( 13, 64)( 14, 63)( 15, 62)( 16, 94)( 17, 93)( 18, 92)
( 19, 91)( 20, 95)( 21,124)( 22,123)( 23,122)( 24,121)( 25,125)( 26,101)
( 27,105)( 28,104)( 29,103)( 30,102)( 37, 40)( 38, 39)( 41, 69)( 42, 68)
( 43, 67)( 44, 66)( 45, 70)( 46, 99)( 47, 98)( 48, 97)( 49, 96)( 50,100)
( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56,110)( 57,109)( 58,108)
( 59,107)( 60,106)( 71, 74)( 72, 73)( 81, 85)( 82, 84)( 86,111)( 87,115)
( 88,114)( 89,113)( 90,112)(116,119)(117,118);
s1 := Sym(125)!(  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26, 41)( 27, 45)( 28, 44)
( 29, 43)( 30, 42)( 31, 36)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 50)
( 48, 49)( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)
( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 99)( 77, 98)( 78, 97)
( 79, 96)( 80,100)( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 85, 95)( 86, 89)
( 87, 88)(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)
(116,122)(117,121)(118,125)(119,124)(120,123);
s2 := Sym(125)!(  1, 36)(  2, 40)(  3, 39)(  4, 38)(  5, 37)(  6, 10)(  7,  9)
( 11,101)( 12,105)( 13,104)( 14,103)( 15,102)( 16, 99)( 17, 98)( 18, 97)
( 19, 96)( 20,100)( 21, 69)( 22, 68)( 23, 67)( 24, 66)( 25, 70)( 26, 61)
( 27, 65)( 28, 64)( 29, 63)( 30, 62)( 31, 35)( 32, 34)( 41,124)( 42,123)
( 43,122)( 44,121)( 45,125)( 46, 94)( 47, 93)( 48, 92)( 49, 91)( 50, 95)
( 51, 86)( 52, 90)( 53, 89)( 54, 88)( 55, 87)( 56, 60)( 57, 59)( 71,119)
( 72,118)( 73,117)( 74,116)( 75,120)( 76,111)( 77,115)( 78,114)( 79,113)
( 80,112)( 81, 85)( 82, 84)(106,110)(107,109);
poly := sub<Sym(125)|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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 >;

References : None.
to this polytope