Polytope of Type {2,34,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,34,10}*1360
if this polytope has a name.
Group : SmallGroup(1360,241)
Rank : 4
Schlafli Type : {2,34,10}
Number of vertices, edges, etc : 2, 34, 170, 10
Order of s₀s₁s₂s₃ : 170
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,34,2}*272
   10-fold quotients : {2,17,2}*136
   17-fold quotients : {2,2,10}*80
   34-fold quotients : {2,2,5}*40
   85-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 19)(  5, 18)(  6, 17)(  7, 16)(  8, 15)(  9, 14)( 10, 13)( 11, 12)
( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 45, 46)
( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)( 61, 64)( 62, 63)
( 72, 87)( 73, 86)( 74, 85)( 75, 84)( 76, 83)( 77, 82)( 78, 81)( 79, 80)
( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)
(106,121)(107,120)(108,119)(109,118)(110,117)(111,116)(112,115)(113,114)
(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131)
(140,155)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)
(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)(164,165);;
s2 := (  3,  4)(  5, 19)(  6, 18)(  7, 17)(  8, 16)(  9, 15)( 10, 14)( 11, 13)
( 20, 72)( 21, 71)( 22, 87)( 23, 86)( 24, 85)( 25, 84)( 26, 83)( 27, 82)
( 28, 81)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 76)( 34, 75)( 35, 74)
( 36, 73)( 37, 55)( 38, 54)( 39, 70)( 40, 69)( 41, 68)( 42, 67)( 43, 66)
( 44, 65)( 45, 64)( 46, 63)( 47, 62)( 48, 61)( 49, 60)( 50, 59)( 51, 58)
( 52, 57)( 53, 56)( 88, 89)( 90,104)( 91,103)( 92,102)( 93,101)( 94,100)
( 95, 99)( 96, 98)(105,157)(106,156)(107,172)(108,171)(109,170)(110,169)
(111,168)(112,167)(113,166)(114,165)(115,164)(116,163)(117,162)(118,161)
(119,160)(120,159)(121,158)(122,140)(123,139)(124,155)(125,154)(126,153)
(127,152)(128,151)(129,150)(130,149)(131,148)(132,147)(133,146)(134,145)
(135,144)(136,143)(137,142)(138,141);;
s3 := (  3,105)(  4,106)(  5,107)(  6,108)(  7,109)(  8,110)(  9,111)( 10,112)
( 11,113)( 12,114)( 13,115)( 14,116)( 15,117)( 16,118)( 17,119)( 18,120)
( 19,121)( 20, 88)( 21, 89)( 22, 90)( 23, 91)( 24, 92)( 25, 93)( 26, 94)
( 27, 95)( 28, 96)( 29, 97)( 30, 98)( 31, 99)( 32,100)( 33,101)( 34,102)
( 35,103)( 36,104)( 37,156)( 38,157)( 39,158)( 40,159)( 41,160)( 42,161)
( 43,162)( 44,163)( 45,164)( 46,165)( 47,166)( 48,167)( 49,168)( 50,169)
( 51,170)( 52,171)( 53,172)( 54,139)( 55,140)( 56,141)( 57,142)( 58,143)
( 59,144)( 60,145)( 61,146)( 62,147)( 63,148)( 64,149)( 65,150)( 66,151)
( 67,152)( 68,153)( 69,154)( 70,155)( 71,122)( 72,123)( 73,124)( 74,125)
( 75,126)( 76,127)( 77,128)( 78,129)( 79,130)( 80,131)( 81,132)( 82,133)
( 83,134)( 84,135)( 85,136)( 86,137)( 87,138);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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(172)!(1,2);
s1 := Sym(172)!(  4, 19)(  5, 18)(  6, 17)(  7, 16)(  8, 15)(  9, 14)( 10, 13)
( 11, 12)( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)
( 28, 29)( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)
( 45, 46)( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)( 61, 64)
( 62, 63)( 72, 87)( 73, 86)( 74, 85)( 75, 84)( 76, 83)( 77, 82)( 78, 81)
( 79, 80)( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)
( 96, 97)(106,121)(107,120)(108,119)(109,118)(110,117)(111,116)(112,115)
(113,114)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)
(130,131)(140,155)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)
(147,148)(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)
(164,165);
s2 := Sym(172)!(  3,  4)(  5, 19)(  6, 18)(  7, 17)(  8, 16)(  9, 15)( 10, 14)
( 11, 13)( 20, 72)( 21, 71)( 22, 87)( 23, 86)( 24, 85)( 25, 84)( 26, 83)
( 27, 82)( 28, 81)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 76)( 34, 75)
( 35, 74)( 36, 73)( 37, 55)( 38, 54)( 39, 70)( 40, 69)( 41, 68)( 42, 67)
( 43, 66)( 44, 65)( 45, 64)( 46, 63)( 47, 62)( 48, 61)( 49, 60)( 50, 59)
( 51, 58)( 52, 57)( 53, 56)( 88, 89)( 90,104)( 91,103)( 92,102)( 93,101)
( 94,100)( 95, 99)( 96, 98)(105,157)(106,156)(107,172)(108,171)(109,170)
(110,169)(111,168)(112,167)(113,166)(114,165)(115,164)(116,163)(117,162)
(118,161)(119,160)(120,159)(121,158)(122,140)(123,139)(124,155)(125,154)
(126,153)(127,152)(128,151)(129,150)(130,149)(131,148)(132,147)(133,146)
(134,145)(135,144)(136,143)(137,142)(138,141);
s3 := Sym(172)!(  3,105)(  4,106)(  5,107)(  6,108)(  7,109)(  8,110)(  9,111)
( 10,112)( 11,113)( 12,114)( 13,115)( 14,116)( 15,117)( 16,118)( 17,119)
( 18,120)( 19,121)( 20, 88)( 21, 89)( 22, 90)( 23, 91)( 24, 92)( 25, 93)
( 26, 94)( 27, 95)( 28, 96)( 29, 97)( 30, 98)( 31, 99)( 32,100)( 33,101)
( 34,102)( 35,103)( 36,104)( 37,156)( 38,157)( 39,158)( 40,159)( 41,160)
( 42,161)( 43,162)( 44,163)( 45,164)( 46,165)( 47,166)( 48,167)( 49,168)
( 50,169)( 51,170)( 52,171)( 53,172)( 54,139)( 55,140)( 56,141)( 57,142)
( 58,143)( 59,144)( 60,145)( 61,146)( 62,147)( 63,148)( 64,149)( 65,150)
( 66,151)( 67,152)( 68,153)( 69,154)( 70,155)( 71,122)( 72,123)( 73,124)
( 74,125)( 75,126)( 76,127)( 77,128)( 78,129)( 79,130)( 80,131)( 81,132)
( 82,133)( 83,134)( 84,135)( 85,136)( 86,137)( 87,138);
poly := sub<Sym(172)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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 >;

to this polytope