Polytope of Type {30,3}

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

References : None.
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