Polytope of Type {3,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,10}*1500
if this polytope has a name.
Group : SmallGroup(1500,37)
Rank : 3
Schlafli Type : {3,10}
Number of vertices, edges, etc : 75, 375, 250
Order of s₀s₁s₂ : 30
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, 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,  9)(  7,  8)( 11, 12)( 13, 15)( 16, 20)( 17, 19)
( 21, 23)( 24, 25)( 26,112)( 27,111)( 28,115)( 29,114)( 30,113)( 31,120)
( 32,119)( 33,118)( 34,117)( 35,116)( 36,123)( 37,122)( 38,121)( 39,125)
( 40,124)( 41,101)( 42,105)( 43,104)( 44,103)( 45,102)( 46,109)( 47,108)
( 48,107)( 49,106)( 50,110)( 51, 99)( 52, 98)( 53, 97)( 54, 96)( 55,100)
( 56, 77)( 57, 76)( 58, 80)( 59, 79)( 60, 78)( 61, 85)( 62, 84)( 63, 83)
( 64, 82)( 65, 81)( 66, 88)( 67, 87)( 68, 86)( 69, 90)( 70, 89)( 71, 91)
( 72, 95)( 73, 94)( 74, 93)( 75, 92);;
s2 := (  1, 36)(  2, 37)(  3, 38)(  4, 39)(  5, 40)(  6, 31)(  7, 32)(  8, 33)
(  9, 34)( 10, 35)( 11, 26)( 12, 27)( 13, 28)( 14, 29)( 15, 30)( 16, 46)
( 17, 47)( 18, 48)( 19, 49)( 20, 50)( 21, 41)( 22, 42)( 23, 43)( 24, 44)
( 25, 45)( 51,111)( 52,112)( 53,113)( 54,114)( 55,115)( 56,106)( 57,107)
( 58,108)( 59,109)( 60,110)( 61,101)( 62,102)( 63,103)( 64,104)( 65,105)
( 66,121)( 67,122)( 68,123)( 69,124)( 70,125)( 71,116)( 72,117)( 73,118)
( 74,119)( 75,120)( 76, 86)( 77, 87)( 78, 88)( 79, 89)( 80, 90)( 91, 96)
( 92, 97)( 93, 98)( 94, 99)( 95,100);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*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,  9)(  7,  8)( 11, 12)( 13, 15)( 16, 20)
( 17, 19)( 21, 23)( 24, 25)( 26,112)( 27,111)( 28,115)( 29,114)( 30,113)
( 31,120)( 32,119)( 33,118)( 34,117)( 35,116)( 36,123)( 37,122)( 38,121)
( 39,125)( 40,124)( 41,101)( 42,105)( 43,104)( 44,103)( 45,102)( 46,109)
( 47,108)( 48,107)( 49,106)( 50,110)( 51, 99)( 52, 98)( 53, 97)( 54, 96)
( 55,100)( 56, 77)( 57, 76)( 58, 80)( 59, 79)( 60, 78)( 61, 85)( 62, 84)
( 63, 83)( 64, 82)( 65, 81)( 66, 88)( 67, 87)( 68, 86)( 69, 90)( 70, 89)
( 71, 91)( 72, 95)( 73, 94)( 74, 93)( 75, 92);
s2 := Sym(125)!(  1, 36)(  2, 37)(  3, 38)(  4, 39)(  5, 40)(  6, 31)(  7, 32)
(  8, 33)(  9, 34)( 10, 35)( 11, 26)( 12, 27)( 13, 28)( 14, 29)( 15, 30)
( 16, 46)( 17, 47)( 18, 48)( 19, 49)( 20, 50)( 21, 41)( 22, 42)( 23, 43)
( 24, 44)( 25, 45)( 51,111)( 52,112)( 53,113)( 54,114)( 55,115)( 56,106)
( 57,107)( 58,108)( 59,109)( 60,110)( 61,101)( 62,102)( 63,103)( 64,104)
( 65,105)( 66,121)( 67,122)( 68,123)( 69,124)( 70,125)( 71,116)( 72,117)
( 73,118)( 74,119)( 75,120)( 76, 86)( 77, 87)( 78, 88)( 79, 89)( 80, 90)
( 91, 96)( 92, 97)( 93, 98)( 94, 99)( 95,100);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 >;

References : None.
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