Polytope of Type {15,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,10}*1500f
if this polytope has a name.
Group : SmallGroup(1500,125)
Rank : 3
Schlafli Type : {15,10}
Number of vertices, edges, etc : 75, 375, 50
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 10
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 : {3,10}*300
   125-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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