Part of the Atlas of Small Regular Polytopes

Polytope of Type {170}

Atlas Canonical Name {170}*340

Overview

Group
SmallGroup(340,14)
Rank
2
Schläfli Type
{170}
Vertices, edges, …
170, 170
Order of s0s1
170
Also known as
170-gon, {170}. if this polytope has another name.

Special Properties

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

Quotients maximal quotients in bold

2-fold

5-fold

10-fold

17-fold

34-fold

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

References

None.

to this polytope.