Polytope of Type {2,63,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,63,6}*1512
if this polytope has a name.
Group : SmallGroup(1512,559)
Rank : 4
Schlafli Type : {2,63,6}
Number of vertices, edges, etc : 2, 63, 189, 6
Order of s₀s₁s₂s₃ : 126
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,63,2}*504, {2,21,6}*504
   7-fold quotients : {2,9,6}*216
   9-fold quotients : {2,21,2}*168
   21-fold quotients : {2,9,2}*72, {2,3,6}*72
   27-fold quotients : {2,7,2}*56
   63-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  6, 21)(  7, 23)(  8, 22)(  9, 18)( 10, 20)( 11, 19)( 12, 15)
( 13, 17)( 14, 16)( 24, 47)( 25, 46)( 26, 45)( 27, 65)( 28, 64)( 29, 63)
( 30, 62)( 31, 61)( 32, 60)( 33, 59)( 34, 58)( 35, 57)( 36, 56)( 37, 55)
( 38, 54)( 39, 53)( 40, 52)( 41, 51)( 42, 50)( 43, 49)( 44, 48)( 66,129)
( 67,131)( 68,130)( 69,147)( 70,149)( 71,148)( 72,144)( 73,146)( 74,145)
( 75,141)( 76,143)( 77,142)( 78,138)( 79,140)( 80,139)( 81,135)( 82,137)
( 83,136)( 84,132)( 85,134)( 86,133)( 87,173)( 88,172)( 89,171)( 90,191)
( 91,190)( 92,189)( 93,188)( 94,187)( 95,186)( 96,185)( 97,184)( 98,183)
( 99,182)(100,181)(101,180)(102,179)(103,178)(104,177)(105,176)(106,175)
(107,174)(108,152)(109,151)(110,150)(111,170)(112,169)(113,168)(114,167)
(115,166)(116,165)(117,164)(118,163)(119,162)(120,161)(121,160)(122,159)
(123,158)(124,157)(125,156)(126,155)(127,154)(128,153);;
s2 := (  3, 90)(  4, 92)(  5, 91)(  6, 87)(  7, 89)(  8, 88)(  9,105)( 10,107)
( 11,106)( 12,102)( 13,104)( 14,103)( 15, 99)( 16,101)( 17,100)( 18, 96)
( 19, 98)( 20, 97)( 21, 93)( 22, 95)( 23, 94)( 24, 69)( 25, 71)( 26, 70)
( 27, 66)( 28, 68)( 29, 67)( 30, 84)( 31, 86)( 32, 85)( 33, 81)( 34, 83)
( 35, 82)( 36, 78)( 37, 80)( 38, 79)( 39, 75)( 40, 77)( 41, 76)( 42, 72)
( 43, 74)( 44, 73)( 45,113)( 46,112)( 47,111)( 48,110)( 49,109)( 50,108)
( 51,128)( 52,127)( 53,126)( 54,125)( 55,124)( 56,123)( 57,122)( 58,121)
( 59,120)( 60,119)( 61,118)( 62,117)( 63,116)( 64,115)( 65,114)(129,153)
(130,155)(131,154)(132,150)(133,152)(134,151)(135,168)(136,170)(137,169)
(138,165)(139,167)(140,166)(141,162)(142,164)(143,163)(144,159)(145,161)
(146,160)(147,156)(148,158)(149,157)(171,176)(172,175)(173,174)(177,191)
(178,190)(179,189)(180,188)(181,187)(182,186)(183,185);;
s3 := ( 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)(127,190)(128,191);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s3*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*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*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(191)!(1,2);
s1 := Sym(191)!(  4,  5)(  6, 21)(  7, 23)(  8, 22)(  9, 18)( 10, 20)( 11, 19)
( 12, 15)( 13, 17)( 14, 16)( 24, 47)( 25, 46)( 26, 45)( 27, 65)( 28, 64)
( 29, 63)( 30, 62)( 31, 61)( 32, 60)( 33, 59)( 34, 58)( 35, 57)( 36, 56)
( 37, 55)( 38, 54)( 39, 53)( 40, 52)( 41, 51)( 42, 50)( 43, 49)( 44, 48)
( 66,129)( 67,131)( 68,130)( 69,147)( 70,149)( 71,148)( 72,144)( 73,146)
( 74,145)( 75,141)( 76,143)( 77,142)( 78,138)( 79,140)( 80,139)( 81,135)
( 82,137)( 83,136)( 84,132)( 85,134)( 86,133)( 87,173)( 88,172)( 89,171)
( 90,191)( 91,190)( 92,189)( 93,188)( 94,187)( 95,186)( 96,185)( 97,184)
( 98,183)( 99,182)(100,181)(101,180)(102,179)(103,178)(104,177)(105,176)
(106,175)(107,174)(108,152)(109,151)(110,150)(111,170)(112,169)(113,168)
(114,167)(115,166)(116,165)(117,164)(118,163)(119,162)(120,161)(121,160)
(122,159)(123,158)(124,157)(125,156)(126,155)(127,154)(128,153);
s2 := Sym(191)!(  3, 90)(  4, 92)(  5, 91)(  6, 87)(  7, 89)(  8, 88)(  9,105)
( 10,107)( 11,106)( 12,102)( 13,104)( 14,103)( 15, 99)( 16,101)( 17,100)
( 18, 96)( 19, 98)( 20, 97)( 21, 93)( 22, 95)( 23, 94)( 24, 69)( 25, 71)
( 26, 70)( 27, 66)( 28, 68)( 29, 67)( 30, 84)( 31, 86)( 32, 85)( 33, 81)
( 34, 83)( 35, 82)( 36, 78)( 37, 80)( 38, 79)( 39, 75)( 40, 77)( 41, 76)
( 42, 72)( 43, 74)( 44, 73)( 45,113)( 46,112)( 47,111)( 48,110)( 49,109)
( 50,108)( 51,128)( 52,127)( 53,126)( 54,125)( 55,124)( 56,123)( 57,122)
( 58,121)( 59,120)( 60,119)( 61,118)( 62,117)( 63,116)( 64,115)( 65,114)
(129,153)(130,155)(131,154)(132,150)(133,152)(134,151)(135,168)(136,170)
(137,169)(138,165)(139,167)(140,166)(141,162)(142,164)(143,163)(144,159)
(145,161)(146,160)(147,156)(148,158)(149,157)(171,176)(172,175)(173,174)
(177,191)(178,190)(179,189)(180,188)(181,187)(182,186)(183,185);
s3 := Sym(191)!( 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)(127,190)(128,191);
poly := sub<Sym(191)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*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*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*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 >;

to this polytope