Polytope of Type {2,46,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,46,6}*1104
if this polytope has a name.
Group : SmallGroup(1104,164)
Rank : 4
Schlafli Type : {2,46,6}
Number of vertices, edges, etc : 2, 46, 138, 6
Order of s₀s₁s₂s₃ : 138
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 : {2,46,2}*368
   6-fold quotients : {2,23,2}*184
   23-fold quotients : {2,2,6}*48
   46-fold quotients : {2,2,3}*24
   69-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 25)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)( 10, 19)( 11, 18)
( 12, 17)( 13, 16)( 14, 15)( 27, 48)( 28, 47)( 29, 46)( 30, 45)( 31, 44)
( 32, 43)( 33, 42)( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 50, 71)( 51, 70)
( 52, 69)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 60, 61)( 73, 94)( 74, 93)( 75, 92)( 76, 91)( 77, 90)( 78, 89)( 79, 88)
( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 96,117)( 97,116)( 98,115)( 99,114)
(100,113)(101,112)(102,111)(103,110)(104,109)(105,108)(106,107)(119,140)
(120,139)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)(127,132)
(128,131)(129,130);;
s2 := (  3,  4)(  5, 25)(  6, 24)(  7, 23)(  8, 22)(  9, 21)( 10, 20)( 11, 19)
( 12, 18)( 13, 17)( 14, 16)( 26, 50)( 27, 49)( 28, 71)( 29, 70)( 30, 69)
( 31, 68)( 32, 67)( 33, 66)( 34, 65)( 35, 64)( 36, 63)( 37, 62)( 38, 61)
( 39, 60)( 40, 59)( 41, 58)( 42, 57)( 43, 56)( 44, 55)( 45, 54)( 46, 53)
( 47, 52)( 48, 51)( 72, 73)( 74, 94)( 75, 93)( 76, 92)( 77, 91)( 78, 90)
( 79, 89)( 80, 88)( 81, 87)( 82, 86)( 83, 85)( 95,119)( 96,118)( 97,140)
( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)(105,132)
(106,131)(107,130)(108,129)(109,128)(110,127)(111,126)(112,125)(113,124)
(114,123)(115,122)(116,121)(117,120);;
s3 := (  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)( 24,116)( 25,117)( 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, 93)( 48, 94)( 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)( 70,139)( 71,140);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(140)!(1,2);
s1 := Sym(140)!(  4, 25)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)( 10, 19)
( 11, 18)( 12, 17)( 13, 16)( 14, 15)( 27, 48)( 28, 47)( 29, 46)( 30, 45)
( 31, 44)( 32, 43)( 33, 42)( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 50, 71)
( 51, 70)( 52, 69)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)
( 59, 62)( 60, 61)( 73, 94)( 74, 93)( 75, 92)( 76, 91)( 77, 90)( 78, 89)
( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 96,117)( 97,116)( 98,115)
( 99,114)(100,113)(101,112)(102,111)(103,110)(104,109)(105,108)(106,107)
(119,140)(120,139)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)
(127,132)(128,131)(129,130);
s2 := Sym(140)!(  3,  4)(  5, 25)(  6, 24)(  7, 23)(  8, 22)(  9, 21)( 10, 20)
( 11, 19)( 12, 18)( 13, 17)( 14, 16)( 26, 50)( 27, 49)( 28, 71)( 29, 70)
( 30, 69)( 31, 68)( 32, 67)( 33, 66)( 34, 65)( 35, 64)( 36, 63)( 37, 62)
( 38, 61)( 39, 60)( 40, 59)( 41, 58)( 42, 57)( 43, 56)( 44, 55)( 45, 54)
( 46, 53)( 47, 52)( 48, 51)( 72, 73)( 74, 94)( 75, 93)( 76, 92)( 77, 91)
( 78, 90)( 79, 89)( 80, 88)( 81, 87)( 82, 86)( 83, 85)( 95,119)( 96,118)
( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)
(105,132)(106,131)(107,130)(108,129)(109,128)(110,127)(111,126)(112,125)
(113,124)(114,123)(115,122)(116,121)(117,120);
s3 := Sym(140)!(  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)( 24,116)( 25,117)
( 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, 93)( 48, 94)( 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)( 70,139)( 71,140);
poly := sub<Sym(140)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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