Polytope of Type {21,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {21,14}*588
if this polytope has a name.
Group : SmallGroup(588,52)
Rank : 3
Schlafli Type : {21,14}
Number of vertices, edges, etc : 21, 147, 14
Order of s₀s₁s₂ : 42
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {21,14,2} of size 1176
Vertex Figure Of :
   {2,21,14} of size 1176
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {7,14}*196
   7-fold quotients : {21,2}*84
   21-fold quotients : {7,2}*28
   49-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {42,14}*1176c
   3-fold covers : {63,14}*1764, {21,42}*1764
Permutation Representation (GAP) :

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