Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,21,14}

Atlas Canonical Name {2,21,14}*1176

Overview

Group
SmallGroup(1176,265)
Rank
4
Schläfli Type
{2,21,14}
Vertices, edges, …
2, 21, 147, 14
Order of s0s1s2s3
42
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

7-fold

21-fold

49-fold

Covers minimal covers in bold

None in this atlas.

Representations

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*s1*s2*s1*s2*s1*s2*s1*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 ];;
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*s1*s2*s1*s2*s1*s2*s1*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 >;