Part of the Atlas of Small Regular Polytopes

Polytope of Type {174}

Atlas Canonical Name {174}*348

Overview

Group
SmallGroup(348,11)
Rank
2
Schläfli Type
{174}
Vertices, edges, …
174, 174
Order of s0s1
174
Also known as
174-gon, {174}. if this polytope has another name.

Special Properties

  • Universal
  • Spherical
  • Locally Spherical
  • Orientable
  • Self-Dual

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

29-fold

58-fold

87-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := (  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 30, 59)( 31, 87)( 32, 86)( 33, 85)( 34, 84)( 35, 83)( 36, 82)( 37, 81)( 38, 80)( 39, 79)( 40, 78)( 41, 77)( 42, 76)( 43, 75)( 44, 74)( 45, 73)( 46, 72)( 47, 71)( 48, 70)( 49, 69)( 50, 68)( 51, 67)( 52, 66)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)( 99,106)(100,105)(101,104)(102,103)(117,146)(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)(124,168)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157)(136,156)(137,155)(138,154)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147);;
s1 := (  1,118)(  2,117)(  3,145)(  4,144)(  5,143)(  6,142)(  7,141)(  8,140)(  9,139)( 10,138)( 11,137)( 12,136)( 13,135)( 14,134)( 15,133)( 16,132)( 17,131)( 18,130)( 19,129)( 20,128)( 21,127)( 22,126)( 23,125)( 24,124)( 25,123)( 26,122)( 27,121)( 28,120)( 29,119)( 30, 89)( 31, 88)( 32,116)( 33,115)( 34,114)( 35,113)( 36,112)( 37,111)( 38,110)( 39,109)( 40,108)( 41,107)( 42,106)( 43,105)( 44,104)( 45,103)( 46,102)( 47,101)( 48,100)( 49, 99)( 50, 98)( 51, 97)( 52, 96)( 53, 95)( 54, 94)( 55, 93)( 56, 92)( 57, 91)( 58, 90)( 59,147)( 60,146)( 61,174)( 62,173)( 63,172)( 64,171)( 65,170)( 66,169)( 67,168)( 68,167)( 69,166)( 70,165)( 71,164)( 72,163)( 73,162)( 74,161)( 75,160)( 76,159)( 77,158)( 78,157)( 79,156)( 80,155)( 81,154)( 82,153)( 83,152)( 84,151)( 85,150)( 86,149)( 87,148);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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*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*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*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*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*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*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(174)!(  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 30, 59)( 31, 87)( 32, 86)( 33, 85)( 34, 84)( 35, 83)( 36, 82)( 37, 81)( 38, 80)( 39, 79)( 40, 78)( 41, 77)( 42, 76)( 43, 75)( 44, 74)( 45, 73)( 46, 72)( 47, 71)( 48, 70)( 49, 69)( 50, 68)( 51, 67)( 52, 66)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)( 99,106)(100,105)(101,104)(102,103)(117,146)(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)(124,168)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157)(136,156)(137,155)(138,154)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147);
s1 := Sym(174)!(  1,118)(  2,117)(  3,145)(  4,144)(  5,143)(  6,142)(  7,141)(  8,140)(  9,139)( 10,138)( 11,137)( 12,136)( 13,135)( 14,134)( 15,133)( 16,132)( 17,131)( 18,130)( 19,129)( 20,128)( 21,127)( 22,126)( 23,125)( 24,124)( 25,123)( 26,122)( 27,121)( 28,120)( 29,119)( 30, 89)( 31, 88)( 32,116)( 33,115)( 34,114)( 35,113)( 36,112)( 37,111)( 38,110)( 39,109)( 40,108)( 41,107)( 42,106)( 43,105)( 44,104)( 45,103)( 46,102)( 47,101)( 48,100)( 49, 99)( 50, 98)( 51, 97)( 52, 96)( 53, 95)( 54, 94)( 55, 93)( 56, 92)( 57, 91)( 58, 90)( 59,147)( 60,146)( 61,174)( 62,173)( 63,172)( 64,171)( 65,170)( 66,169)( 67,168)( 68,167)( 69,166)( 70,165)( 71,164)( 72,163)( 73,162)( 74,161)( 75,160)( 76,159)( 77,158)( 78,157)( 79,156)( 80,155)( 81,154)( 82,153)( 83,152)( 84,151)( 85,150)( 86,149)( 87,148);
poly := sub<Sym(174)|s0,s1>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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*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*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.