Polytope of Type {46,6}

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

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