Polytope of Type {2,14,21}

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

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

Permutation Representation (Magma) :

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

to this polytope