Polytope of Type {10,25}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,25}*500
if this polytope has a name.
Group : SmallGroup(500,26)
Rank : 3
Schlafli Type : {10,25}
Number of vertices, edges, etc : 10, 125, 25
Order of s₀s₁s₂ : 50
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,25,2} of size 1000
Vertex Figure Of :
   {2,10,25} of size 1000
   {4,10,25} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,25}*100, {10,5}*100
   25-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,50}*1000b
   3-fold covers : {10,75}*1500
   4-fold covers : {10,100}*2000b, {20,50}*2000b
Permutation Representation (GAP) :

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

References : None.
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