Polytope of Type {6,46}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,46}*552
Also Known As : {6,46|2}. if this polytope has another name.
Group : SmallGroup(552,34)
Rank : 3
Schlafli Type : {6,46}
Number of vertices, edges, etc : 6, 138, 46
Order of s₀s₁s₂ : 138
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,46,2} of size 1104
Vertex Figure Of :
   {2,6,46} of size 1104
   {3,6,46} of size 1656
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,46}*184
   6-fold quotients : {2,23}*92
   23-fold quotients : {6,2}*24
   46-fold quotients : {3,2}*12
   69-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,46}*1104, {6,92}*1104a
   3-fold covers : {18,46}*1656, {6,138}*1656a, {6,138}*1656b
Permutation Representation (GAP) :

s0 := ( 24, 47)( 25, 48)( 26, 49)( 27, 50)( 28, 51)( 29, 52)( 30, 53)( 31, 54)
( 32, 55)( 33, 56)( 34, 57)( 35, 58)( 36, 59)( 37, 60)( 38, 61)( 39, 62)
( 40, 63)( 41, 64)( 42, 65)( 43, 66)( 44, 67)( 45, 68)( 46, 69)( 93,116)
( 94,117)( 95,118)( 96,119)( 97,120)( 98,121)( 99,122)(100,123)(101,124)
(102,125)(103,126)(104,127)(105,128)(106,129)(107,130)(108,131)(109,132)
(110,133)(111,134)(112,135)(113,136)(114,137)(115,138);;
s1 := (  1, 24)(  2, 46)(  3, 45)(  4, 44)(  5, 43)(  6, 42)(  7, 41)(  8, 40)
(  9, 39)( 10, 38)( 11, 37)( 12, 36)( 13, 35)( 14, 34)( 15, 33)( 16, 32)
( 17, 31)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 48, 69)
( 49, 68)( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)
( 57, 60)( 58, 59)( 70, 93)( 71,115)( 72,114)( 73,113)( 74,112)( 75,111)
( 76,110)( 77,109)( 78,108)( 79,107)( 80,106)( 81,105)( 82,104)( 83,103)
( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 98)( 89, 97)( 90, 96)( 91, 95)
( 92, 94)(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)
(124,131)(125,130)(126,129)(127,128);;
s2 := (  1, 71)(  2, 70)(  3, 92)(  4, 91)(  5, 90)(  6, 89)(  7, 88)(  8, 87)
(  9, 86)( 10, 85)( 11, 84)( 12, 83)( 13, 82)( 14, 81)( 15, 80)( 16, 79)
( 17, 78)( 18, 77)( 19, 76)( 20, 75)( 21, 74)( 22, 73)( 23, 72)( 24, 94)
( 25, 93)( 26,115)( 27,114)( 28,113)( 29,112)( 30,111)( 31,110)( 32,109)
( 33,108)( 34,107)( 35,106)( 36,105)( 37,104)( 38,103)( 39,102)( 40,101)
( 41,100)( 42, 99)( 43, 98)( 44, 97)( 45, 96)( 46, 95)( 47,117)( 48,116)
( 49,138)( 50,137)( 51,136)( 52,135)( 53,134)( 54,133)( 55,132)( 56,131)
( 57,130)( 58,129)( 59,128)( 60,127)( 61,126)( 62,125)( 63,124)( 64,123)
( 65,122)( 66,121)( 67,120)( 68,119)( 69,118);;
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*s2*s1*s0*s1*s2*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*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(138)!( 24, 47)( 25, 48)( 26, 49)( 27, 50)( 28, 51)( 29, 52)( 30, 53)
( 31, 54)( 32, 55)( 33, 56)( 34, 57)( 35, 58)( 36, 59)( 37, 60)( 38, 61)
( 39, 62)( 40, 63)( 41, 64)( 42, 65)( 43, 66)( 44, 67)( 45, 68)( 46, 69)
( 93,116)( 94,117)( 95,118)( 96,119)( 97,120)( 98,121)( 99,122)(100,123)
(101,124)(102,125)(103,126)(104,127)(105,128)(106,129)(107,130)(108,131)
(109,132)(110,133)(111,134)(112,135)(113,136)(114,137)(115,138);
s1 := Sym(138)!(  1, 24)(  2, 46)(  3, 45)(  4, 44)(  5, 43)(  6, 42)(  7, 41)
(  8, 40)(  9, 39)( 10, 38)( 11, 37)( 12, 36)( 13, 35)( 14, 34)( 15, 33)
( 16, 32)( 17, 31)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)
( 48, 69)( 49, 68)( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)
( 56, 61)( 57, 60)( 58, 59)( 70, 93)( 71,115)( 72,114)( 73,113)( 74,112)
( 75,111)( 76,110)( 77,109)( 78,108)( 79,107)( 80,106)( 81,105)( 82,104)
( 83,103)( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 98)( 89, 97)( 90, 96)
( 91, 95)( 92, 94)(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)
(123,132)(124,131)(125,130)(126,129)(127,128);
s2 := Sym(138)!(  1, 71)(  2, 70)(  3, 92)(  4, 91)(  5, 90)(  6, 89)(  7, 88)
(  8, 87)(  9, 86)( 10, 85)( 11, 84)( 12, 83)( 13, 82)( 14, 81)( 15, 80)
( 16, 79)( 17, 78)( 18, 77)( 19, 76)( 20, 75)( 21, 74)( 22, 73)( 23, 72)
( 24, 94)( 25, 93)( 26,115)( 27,114)( 28,113)( 29,112)( 30,111)( 31,110)
( 32,109)( 33,108)( 34,107)( 35,106)( 36,105)( 37,104)( 38,103)( 39,102)
( 40,101)( 41,100)( 42, 99)( 43, 98)( 44, 97)( 45, 96)( 46, 95)( 47,117)
( 48,116)( 49,138)( 50,137)( 51,136)( 52,135)( 53,134)( 54,133)( 55,132)
( 56,131)( 57,130)( 58,129)( 59,128)( 60,127)( 61,126)( 62,125)( 63,124)
( 64,123)( 65,122)( 66,121)( 67,120)( 68,119)( 69,118);
poly := sub<Sym(138)|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*s2*s1*s0*s1*s2*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*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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