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Polytope of Type {6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,10}*600a
if this polytope has a name.
Group : SmallGroup(600,154)
Rank : 3
Schlafli Type : {6,10}
Number of vertices, edges, etc : 30, 150, 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 :
   {6,10,2} of size 1200
Vertex Figure Of :
   {2,6,10} of size 1200
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,10}*300
   25-fold quotients : {6,2}*24
   50-fold quotients : {3,2}*12
   75-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,20}*1200a, {12,10}*1200b
   3-fold covers : {18,10}*1800a, {6,30}*1800b, {6,30}*1800c
Permutation Representation (GAP) :
s0 := (  2,  7)(  3, 13)(  4, 19)(  5, 25)(  6, 21)(  9, 14)( 10, 20)( 11, 16)
( 12, 22)( 18, 23)( 26, 51)( 27, 57)( 28, 63)( 29, 69)( 30, 75)( 31, 71)
( 32, 52)( 33, 58)( 34, 64)( 35, 70)( 36, 66)( 37, 72)( 38, 53)( 39, 59)
( 40, 65)( 41, 61)( 42, 67)( 43, 73)( 44, 54)( 45, 60)( 46, 56)( 47, 62)
( 48, 68)( 49, 74)( 50, 55)( 77, 82)( 78, 88)( 79, 94)( 80,100)( 81, 96)
( 84, 89)( 85, 95)( 86, 91)( 87, 97)( 93, 98)(101,126)(102,132)(103,138)
(104,144)(105,150)(106,146)(107,127)(108,133)(109,139)(110,145)(111,141)
(112,147)(113,128)(114,134)(115,140)(116,136)(117,142)(118,148)(119,129)
(120,135)(121,131)(122,137)(123,143)(124,149)(125,130);;
s1 := (  1, 26)(  2, 33)(  3, 40)(  4, 42)(  5, 49)(  6, 43)(  7, 50)(  8, 27)
(  9, 34)( 10, 36)( 11, 35)( 12, 37)( 13, 44)( 14, 46)( 15, 28)( 16, 47)
( 17, 29)( 18, 31)( 19, 38)( 20, 45)( 21, 39)( 22, 41)( 23, 48)( 24, 30)
( 25, 32)( 52, 58)( 53, 65)( 54, 67)( 55, 74)( 56, 68)( 57, 75)( 60, 61)
( 63, 69)( 64, 71)( 66, 72)( 76,101)( 77,108)( 78,115)( 79,117)( 80,124)
( 81,118)( 82,125)( 83,102)( 84,109)( 85,111)( 86,110)( 87,112)( 88,119)
( 89,121)( 90,103)( 91,122)( 92,104)( 93,106)( 94,113)( 95,120)( 96,114)
( 97,116)( 98,123)( 99,105)(100,107)(127,133)(128,140)(129,142)(130,149)
(131,143)(132,150)(135,136)(138,144)(139,146)(141,147);;
s2 := (  1, 83)(  2, 82)(  3, 81)(  4, 85)(  5, 84)(  6, 78)(  7, 77)(  8, 76)
(  9, 80)( 10, 79)( 11, 98)( 12, 97)( 13, 96)( 14,100)( 15, 99)( 16, 93)
( 17, 92)( 18, 91)( 19, 95)( 20, 94)( 21, 88)( 22, 87)( 23, 86)( 24, 90)
( 25, 89)( 26,108)( 27,107)( 28,106)( 29,110)( 30,109)( 31,103)( 32,102)
( 33,101)( 34,105)( 35,104)( 36,123)( 37,122)( 38,121)( 39,125)( 40,124)
( 41,118)( 42,117)( 43,116)( 44,120)( 45,119)( 46,113)( 47,112)( 48,111)
( 49,115)( 50,114)( 51,133)( 52,132)( 53,131)( 54,135)( 55,134)( 56,128)
( 57,127)( 58,126)( 59,130)( 60,129)( 61,148)( 62,147)( 63,146)( 64,150)
( 65,149)( 66,143)( 67,142)( 68,141)( 69,145)( 70,144)( 71,138)( 72,137)
( 73,136)( 74,140)( 75,139);;
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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
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(150)!(  2,  7)(  3, 13)(  4, 19)(  5, 25)(  6, 21)(  9, 14)( 10, 20)
( 11, 16)( 12, 22)( 18, 23)( 26, 51)( 27, 57)( 28, 63)( 29, 69)( 30, 75)
( 31, 71)( 32, 52)( 33, 58)( 34, 64)( 35, 70)( 36, 66)( 37, 72)( 38, 53)
( 39, 59)( 40, 65)( 41, 61)( 42, 67)( 43, 73)( 44, 54)( 45, 60)( 46, 56)
( 47, 62)( 48, 68)( 49, 74)( 50, 55)( 77, 82)( 78, 88)( 79, 94)( 80,100)
( 81, 96)( 84, 89)( 85, 95)( 86, 91)( 87, 97)( 93, 98)(101,126)(102,132)
(103,138)(104,144)(105,150)(106,146)(107,127)(108,133)(109,139)(110,145)
(111,141)(112,147)(113,128)(114,134)(115,140)(116,136)(117,142)(118,148)
(119,129)(120,135)(121,131)(122,137)(123,143)(124,149)(125,130);
s1 := Sym(150)!(  1, 26)(  2, 33)(  3, 40)(  4, 42)(  5, 49)(  6, 43)(  7, 50)
(  8, 27)(  9, 34)( 10, 36)( 11, 35)( 12, 37)( 13, 44)( 14, 46)( 15, 28)
( 16, 47)( 17, 29)( 18, 31)( 19, 38)( 20, 45)( 21, 39)( 22, 41)( 23, 48)
( 24, 30)( 25, 32)( 52, 58)( 53, 65)( 54, 67)( 55, 74)( 56, 68)( 57, 75)
( 60, 61)( 63, 69)( 64, 71)( 66, 72)( 76,101)( 77,108)( 78,115)( 79,117)
( 80,124)( 81,118)( 82,125)( 83,102)( 84,109)( 85,111)( 86,110)( 87,112)
( 88,119)( 89,121)( 90,103)( 91,122)( 92,104)( 93,106)( 94,113)( 95,120)
( 96,114)( 97,116)( 98,123)( 99,105)(100,107)(127,133)(128,140)(129,142)
(130,149)(131,143)(132,150)(135,136)(138,144)(139,146)(141,147);
s2 := Sym(150)!(  1, 83)(  2, 82)(  3, 81)(  4, 85)(  5, 84)(  6, 78)(  7, 77)
(  8, 76)(  9, 80)( 10, 79)( 11, 98)( 12, 97)( 13, 96)( 14,100)( 15, 99)
( 16, 93)( 17, 92)( 18, 91)( 19, 95)( 20, 94)( 21, 88)( 22, 87)( 23, 86)
( 24, 90)( 25, 89)( 26,108)( 27,107)( 28,106)( 29,110)( 30,109)( 31,103)
( 32,102)( 33,101)( 34,105)( 35,104)( 36,123)( 37,122)( 38,121)( 39,125)
( 40,124)( 41,118)( 42,117)( 43,116)( 44,120)( 45,119)( 46,113)( 47,112)
( 48,111)( 49,115)( 50,114)( 51,133)( 52,132)( 53,131)( 54,135)( 55,134)
( 56,128)( 57,127)( 58,126)( 59,130)( 60,129)( 61,148)( 62,147)( 63,146)
( 64,150)( 65,149)( 66,143)( 67,142)( 68,141)( 69,145)( 70,144)( 71,138)
( 72,137)( 73,136)( 74,140)( 75,139);
poly := sub<Sym(150)|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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
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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