Polytope of Type {63,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {63,6}*756
if this polytope has a name.
Group : SmallGroup(756,96)
Rank : 3
Schlafli Type : {63,6}
Number of vertices, edges, etc : 63, 189, 6
Order of s₀s₁s₂ : 126
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {63,6,2} of size 1512
Vertex Figure Of :
   {2,63,6} of size 1512
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {63,2}*252, {21,6}*252
   7-fold quotients : {9,6}*108
   9-fold quotients : {21,2}*84
   21-fold quotients : {9,2}*36, {3,6}*36
   27-fold quotients : {7,2}*28
   63-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {126,6}*1512b
Permutation Representation (GAP) :

s0 := (  2,  3)(  4, 19)(  5, 21)(  6, 20)(  7, 16)(  8, 18)(  9, 17)( 10, 13)
( 11, 15)( 12, 14)( 22, 45)( 23, 44)( 24, 43)( 25, 63)( 26, 62)( 27, 61)
( 28, 60)( 29, 59)( 30, 58)( 31, 57)( 32, 56)( 33, 55)( 34, 54)( 35, 53)
( 36, 52)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 64,127)
( 65,129)( 66,128)( 67,145)( 68,147)( 69,146)( 70,142)( 71,144)( 72,143)
( 73,139)( 74,141)( 75,140)( 76,136)( 77,138)( 78,137)( 79,133)( 80,135)
( 81,134)( 82,130)( 83,132)( 84,131)( 85,171)( 86,170)( 87,169)( 88,189)
( 89,188)( 90,187)( 91,186)( 92,185)( 93,184)( 94,183)( 95,182)( 96,181)
( 97,180)( 98,179)( 99,178)(100,177)(101,176)(102,175)(103,174)(104,173)
(105,172)(106,150)(107,149)(108,148)(109,168)(110,167)(111,166)(112,165)
(113,164)(114,163)(115,162)(116,161)(117,160)(118,159)(119,158)(120,157)
(121,156)(122,155)(123,154)(124,153)(125,152)(126,151);;
s1 := (  1, 88)(  2, 90)(  3, 89)(  4, 85)(  5, 87)(  6, 86)(  7,103)(  8,105)
(  9,104)( 10,100)( 11,102)( 12,101)( 13, 97)( 14, 99)( 15, 98)( 16, 94)
( 17, 96)( 18, 95)( 19, 91)( 20, 93)( 21, 92)( 22, 67)( 23, 69)( 24, 68)
( 25, 64)( 26, 66)( 27, 65)( 28, 82)( 29, 84)( 30, 83)( 31, 79)( 32, 81)
( 33, 80)( 34, 76)( 35, 78)( 36, 77)( 37, 73)( 38, 75)( 39, 74)( 40, 70)
( 41, 72)( 42, 71)( 43,111)( 44,110)( 45,109)( 46,108)( 47,107)( 48,106)
( 49,126)( 50,125)( 51,124)( 52,123)( 53,122)( 54,121)( 55,120)( 56,119)
( 57,118)( 58,117)( 59,116)( 60,115)( 61,114)( 62,113)( 63,112)(127,151)
(128,153)(129,152)(130,148)(131,150)(132,149)(133,166)(134,168)(135,167)
(136,163)(137,165)(138,164)(139,160)(140,162)(141,161)(142,157)(143,159)
(144,158)(145,154)(146,156)(147,155)(169,174)(170,173)(171,172)(175,189)
(176,188)(177,187)(178,186)(179,185)(180,184)(181,183);;
s2 := ( 64,127)( 65,128)( 66,129)( 67,130)( 68,131)( 69,132)( 70,133)( 71,134)
( 72,135)( 73,136)( 74,137)( 75,138)( 76,139)( 77,140)( 78,141)( 79,142)
( 80,143)( 81,144)( 82,145)( 83,146)( 84,147)( 85,148)( 86,149)( 87,150)
( 88,151)( 89,152)( 90,153)( 91,154)( 92,155)( 93,156)( 94,157)( 95,158)
( 96,159)( 97,160)( 98,161)( 99,162)(100,163)(101,164)(102,165)(103,166)
(104,167)(105,168)(106,169)(107,170)(108,171)(109,172)(110,173)(111,174)
(112,175)(113,176)(114,177)(115,178)(116,179)(117,180)(118,181)(119,182)
(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189);;
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*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(189)!(  2,  3)(  4, 19)(  5, 21)(  6, 20)(  7, 16)(  8, 18)(  9, 17)
( 10, 13)( 11, 15)( 12, 14)( 22, 45)( 23, 44)( 24, 43)( 25, 63)( 26, 62)
( 27, 61)( 28, 60)( 29, 59)( 30, 58)( 31, 57)( 32, 56)( 33, 55)( 34, 54)
( 35, 53)( 36, 52)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 64,127)( 65,129)( 66,128)( 67,145)( 68,147)( 69,146)( 70,142)( 71,144)
( 72,143)( 73,139)( 74,141)( 75,140)( 76,136)( 77,138)( 78,137)( 79,133)
( 80,135)( 81,134)( 82,130)( 83,132)( 84,131)( 85,171)( 86,170)( 87,169)
( 88,189)( 89,188)( 90,187)( 91,186)( 92,185)( 93,184)( 94,183)( 95,182)
( 96,181)( 97,180)( 98,179)( 99,178)(100,177)(101,176)(102,175)(103,174)
(104,173)(105,172)(106,150)(107,149)(108,148)(109,168)(110,167)(111,166)
(112,165)(113,164)(114,163)(115,162)(116,161)(117,160)(118,159)(119,158)
(120,157)(121,156)(122,155)(123,154)(124,153)(125,152)(126,151);
s1 := Sym(189)!(  1, 88)(  2, 90)(  3, 89)(  4, 85)(  5, 87)(  6, 86)(  7,103)
(  8,105)(  9,104)( 10,100)( 11,102)( 12,101)( 13, 97)( 14, 99)( 15, 98)
( 16, 94)( 17, 96)( 18, 95)( 19, 91)( 20, 93)( 21, 92)( 22, 67)( 23, 69)
( 24, 68)( 25, 64)( 26, 66)( 27, 65)( 28, 82)( 29, 84)( 30, 83)( 31, 79)
( 32, 81)( 33, 80)( 34, 76)( 35, 78)( 36, 77)( 37, 73)( 38, 75)( 39, 74)
( 40, 70)( 41, 72)( 42, 71)( 43,111)( 44,110)( 45,109)( 46,108)( 47,107)
( 48,106)( 49,126)( 50,125)( 51,124)( 52,123)( 53,122)( 54,121)( 55,120)
( 56,119)( 57,118)( 58,117)( 59,116)( 60,115)( 61,114)( 62,113)( 63,112)
(127,151)(128,153)(129,152)(130,148)(131,150)(132,149)(133,166)(134,168)
(135,167)(136,163)(137,165)(138,164)(139,160)(140,162)(141,161)(142,157)
(143,159)(144,158)(145,154)(146,156)(147,155)(169,174)(170,173)(171,172)
(175,189)(176,188)(177,187)(178,186)(179,185)(180,184)(181,183);
s2 := Sym(189)!( 64,127)( 65,128)( 66,129)( 67,130)( 68,131)( 69,132)( 70,133)
( 71,134)( 72,135)( 73,136)( 74,137)( 75,138)( 76,139)( 77,140)( 78,141)
( 79,142)( 80,143)( 81,144)( 82,145)( 83,146)( 84,147)( 85,148)( 86,149)
( 87,150)( 88,151)( 89,152)( 90,153)( 91,154)( 92,155)( 93,156)( 94,157)
( 95,158)( 96,159)( 97,160)( 98,161)( 99,162)(100,163)(101,164)(102,165)
(103,166)(104,167)(105,168)(106,169)(107,170)(108,171)(109,172)(110,173)
(111,174)(112,175)(113,176)(114,177)(115,178)(116,179)(117,180)(118,181)
(119,182)(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189);
poly := sub<Sym(189)|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*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope