Polytope of Type {2,21,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,21,14}*1176
if this polytope has a name.
Group : SmallGroup(1176,265)
Rank : 4
Schlafli Type : {2,21,14}
Number of vertices, edges, etc : 2, 21, 147, 14
Order of s₀s₁s₂s₃ : 42
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 : {2,7,14}*392
   7-fold quotients : {2,21,2}*168
   21-fold quotients : {2,7,2}*56
   49-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 10, 45)( 11, 51)( 12, 50)( 13, 49)( 14, 48)
( 15, 47)( 16, 46)( 17, 38)( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)
( 23, 39)( 24, 31)( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)( 30, 32)
( 52,101)( 53,107)( 54,106)( 55,105)( 56,104)( 57,103)( 58,102)( 59,143)
( 60,149)( 61,148)( 62,147)( 63,146)( 64,145)( 65,144)( 66,136)( 67,142)
( 68,141)( 69,140)( 70,139)( 71,138)( 72,137)( 73,129)( 74,135)( 75,134)
( 76,133)( 77,132)( 78,131)( 79,130)( 80,122)( 81,128)( 82,127)( 83,126)
( 84,125)( 85,124)( 86,123)( 87,115)( 88,121)( 89,120)( 90,119)( 91,118)
( 92,117)( 93,116)( 94,108)( 95,114)( 96,113)( 97,112)( 98,111)( 99,110)
(100,109);;
s2 := (  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)( 10, 53)
( 11, 52)( 12, 58)( 13, 57)( 14, 56)( 15, 55)( 16, 54)( 17, 95)( 18, 94)
( 19,100)( 20, 99)( 21, 98)( 22, 97)( 23, 96)( 24, 88)( 25, 87)( 26, 93)
( 27, 92)( 28, 91)( 29, 90)( 30, 89)( 31, 81)( 32, 80)( 33, 86)( 34, 85)
( 35, 84)( 36, 83)( 37, 82)( 38, 74)( 39, 73)( 40, 79)( 41, 78)( 42, 77)
( 43, 76)( 44, 75)( 45, 67)( 46, 66)( 47, 72)( 48, 71)( 49, 70)( 50, 69)
( 51, 68)(101,109)(102,108)(103,114)(104,113)(105,112)(106,111)(107,110)
(115,144)(116,143)(117,149)(118,148)(119,147)(120,146)(121,145)(122,137)
(123,136)(124,142)(125,141)(126,140)(127,139)(128,138)(129,130)(131,135)
(132,134);;
s3 := ( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 50)( 16, 51)( 17, 38)
( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 43)( 23, 44)( 24, 31)( 25, 32)
( 26, 33)( 27, 34)( 28, 35)( 29, 36)( 30, 37)( 59, 94)( 60, 95)( 61, 96)
( 62, 97)( 63, 98)( 64, 99)( 65,100)( 66, 87)( 67, 88)( 68, 89)( 69, 90)
( 70, 91)( 71, 92)( 72, 93)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)
( 78, 85)( 79, 86)(108,143)(109,144)(110,145)(111,146)(112,147)(113,148)
(114,149)(115,136)(116,137)(117,138)(118,139)(119,140)(120,141)(121,142)
(122,129)(123,130)(124,131)(125,132)(126,133)(127,134)(128,135);;
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*s1*s2*s1*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(149)!(1,2);
s1 := Sym(149)!(  4,  9)(  5,  8)(  6,  7)( 10, 45)( 11, 51)( 12, 50)( 13, 49)
( 14, 48)( 15, 47)( 16, 46)( 17, 38)( 18, 44)( 19, 43)( 20, 42)( 21, 41)
( 22, 40)( 23, 39)( 24, 31)( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 52,101)( 53,107)( 54,106)( 55,105)( 56,104)( 57,103)( 58,102)
( 59,143)( 60,149)( 61,148)( 62,147)( 63,146)( 64,145)( 65,144)( 66,136)
( 67,142)( 68,141)( 69,140)( 70,139)( 71,138)( 72,137)( 73,129)( 74,135)
( 75,134)( 76,133)( 77,132)( 78,131)( 79,130)( 80,122)( 81,128)( 82,127)
( 83,126)( 84,125)( 85,124)( 86,123)( 87,115)( 88,121)( 89,120)( 90,119)
( 91,118)( 92,117)( 93,116)( 94,108)( 95,114)( 96,113)( 97,112)( 98,111)
( 99,110)(100,109);
s2 := Sym(149)!(  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)
( 10, 53)( 11, 52)( 12, 58)( 13, 57)( 14, 56)( 15, 55)( 16, 54)( 17, 95)
( 18, 94)( 19,100)( 20, 99)( 21, 98)( 22, 97)( 23, 96)( 24, 88)( 25, 87)
( 26, 93)( 27, 92)( 28, 91)( 29, 90)( 30, 89)( 31, 81)( 32, 80)( 33, 86)
( 34, 85)( 35, 84)( 36, 83)( 37, 82)( 38, 74)( 39, 73)( 40, 79)( 41, 78)
( 42, 77)( 43, 76)( 44, 75)( 45, 67)( 46, 66)( 47, 72)( 48, 71)( 49, 70)
( 50, 69)( 51, 68)(101,109)(102,108)(103,114)(104,113)(105,112)(106,111)
(107,110)(115,144)(116,143)(117,149)(118,148)(119,147)(120,146)(121,145)
(122,137)(123,136)(124,142)(125,141)(126,140)(127,139)(128,138)(129,130)
(131,135)(132,134);
s3 := Sym(149)!( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 50)( 16, 51)
( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 43)( 23, 44)( 24, 31)
( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 29, 36)( 30, 37)( 59, 94)( 60, 95)
( 61, 96)( 62, 97)( 63, 98)( 64, 99)( 65,100)( 66, 87)( 67, 88)( 68, 89)
( 69, 90)( 70, 91)( 71, 92)( 72, 93)( 73, 80)( 74, 81)( 75, 82)( 76, 83)
( 77, 84)( 78, 85)( 79, 86)(108,143)(109,144)(110,145)(111,146)(112,147)
(113,148)(114,149)(115,136)(116,137)(117,138)(118,139)(119,140)(120,141)
(121,142)(122,129)(123,130)(124,131)(125,132)(126,133)(127,134)(128,135);
poly := sub<Sym(149)|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*s1*s2*s1*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 >;

to this polytope