Polytope of Type {10,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,30}*1500f
if this polytope has a name.
Group : SmallGroup(1500,126)
Rank : 3
Schlafli Type : {10,30}
Number of vertices, edges, etc : 25, 375, 75
Order of s₀s₁s₂ : 15
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {10,6}*300
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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