Polytope of Type {170,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {170,2}*680
if this polytope has a name.
Group : SmallGroup(680,52)
Rank : 3
Schlafli Type : {170,2}
Number of vertices, edges, etc : 170, 170, 2
Order of s0s1s2 : 170
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{170,2,2} of size 1360
Vertex Figure Of :
{2,170,2} of size 1360
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {85,2}*340
5-fold quotients : {34,2}*136
10-fold quotients : {17,2}*68
17-fold quotients : {10,2}*40
34-fold quotients : {5,2}*20
85-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {340,2}*1360, {170,4}*1360
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);;
s2 := (171,172);;
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, s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(172)!( 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(172)!( 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);
s2 := Sym(172)!(171,172);
poly := sub<Sym(172)|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, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope