Polytope of Type {17,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {17,34}*1156
if this polytope has a name.
Group : SmallGroup(1156,13)
Rank : 3
Schlafli Type : {17,34}
Number of vertices, edges, etc : 17, 289, 34
Order of s₀s₁s₂ : 34
Order of s₀s₁s₂s₁ : 34
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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) :
   17-fold quotients : {17,2}*68
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)
( 18,273)( 19,289)( 20,288)( 21,287)( 22,286)( 23,285)( 24,284)( 25,283)
( 26,282)( 27,281)( 28,280)( 29,279)( 30,278)( 31,277)( 32,276)( 33,275)
( 34,274)( 35,256)( 36,272)( 37,271)( 38,270)( 39,269)( 40,268)( 41,267)
( 42,266)( 43,265)( 44,264)( 45,263)( 46,262)( 47,261)( 48,260)( 49,259)
( 50,258)( 51,257)( 52,239)( 53,255)( 54,254)( 55,253)( 56,252)( 57,251)
( 58,250)( 59,249)( 60,248)( 61,247)( 62,246)( 63,245)( 64,244)( 65,243)
( 66,242)( 67,241)( 68,240)( 69,222)( 70,238)( 71,237)( 72,236)( 73,235)
( 74,234)( 75,233)( 76,232)( 77,231)( 78,230)( 79,229)( 80,228)( 81,227)
( 82,226)( 83,225)( 84,224)( 85,223)( 86,205)( 87,221)( 88,220)( 89,219)
( 90,218)( 91,217)( 92,216)( 93,215)( 94,214)( 95,213)( 96,212)( 97,211)
( 98,210)( 99,209)(100,208)(101,207)(102,206)(103,188)(104,204)(105,203)
(106,202)(107,201)(108,200)(109,199)(110,198)(111,197)(112,196)(113,195)
(114,194)(115,193)(116,192)(117,191)(118,190)(119,189)(120,171)(121,187)
(122,186)(123,185)(124,184)(125,183)(126,182)(127,181)(128,180)(129,179)
(130,178)(131,177)(132,176)(133,175)(134,174)(135,173)(136,172)(137,154)
(138,170)(139,169)(140,168)(141,167)(142,166)(143,165)(144,164)(145,163)
(146,162)(147,161)(148,160)(149,159)(150,158)(151,157)(152,156)(153,155);;
s1 := (  1, 19)(  2, 18)(  3, 34)(  4, 33)(  5, 32)(  6, 31)(  7, 30)(  8, 29)
(  9, 28)( 10, 27)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)
( 17, 20)( 35,274)( 36,273)( 37,289)( 38,288)( 39,287)( 40,286)( 41,285)
( 42,284)( 43,283)( 44,282)( 45,281)( 46,280)( 47,279)( 48,278)( 49,277)
( 50,276)( 51,275)( 52,257)( 53,256)( 54,272)( 55,271)( 56,270)( 57,269)
( 58,268)( 59,267)( 60,266)( 61,265)( 62,264)( 63,263)( 64,262)( 65,261)
( 66,260)( 67,259)( 68,258)( 69,240)( 70,239)( 71,255)( 72,254)( 73,253)
( 74,252)( 75,251)( 76,250)( 77,249)( 78,248)( 79,247)( 80,246)( 81,245)
( 82,244)( 83,243)( 84,242)( 85,241)( 86,223)( 87,222)( 88,238)( 89,237)
( 90,236)( 91,235)( 92,234)( 93,233)( 94,232)( 95,231)( 96,230)( 97,229)
( 98,228)( 99,227)(100,226)(101,225)(102,224)(103,206)(104,205)(105,221)
(106,220)(107,219)(108,218)(109,217)(110,216)(111,215)(112,214)(113,213)
(114,212)(115,211)(116,210)(117,209)(118,208)(119,207)(120,189)(121,188)
(122,204)(123,203)(124,202)(125,201)(126,200)(127,199)(128,198)(129,197)
(130,196)(131,195)(132,194)(133,193)(134,192)(135,191)(136,190)(137,172)
(138,171)(139,187)(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)
(146,180)(147,179)(148,178)(149,177)(150,176)(151,175)(152,174)(153,173)
(154,155)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164);;
s2 := (  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)
( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)( 26, 27)
( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)( 43, 44)
( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)( 60, 61)
( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)( 77, 78)
( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)
(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)
(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)
(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)(145,146)
(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)
(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)(179,180)
(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197)
(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)(213,214)
(223,238)(224,237)(225,236)(226,235)(227,234)(228,233)(229,232)(230,231)
(240,255)(241,254)(242,253)(243,252)(244,251)(245,250)(246,249)(247,248)
(257,272)(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)(264,265)
(274,289)(275,288)(276,287)(277,286)(278,285)(279,284)(280,283)(281,282);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(289)!(  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)
(  9, 10)( 18,273)( 19,289)( 20,288)( 21,287)( 22,286)( 23,285)( 24,284)
( 25,283)( 26,282)( 27,281)( 28,280)( 29,279)( 30,278)( 31,277)( 32,276)
( 33,275)( 34,274)( 35,256)( 36,272)( 37,271)( 38,270)( 39,269)( 40,268)
( 41,267)( 42,266)( 43,265)( 44,264)( 45,263)( 46,262)( 47,261)( 48,260)
( 49,259)( 50,258)( 51,257)( 52,239)( 53,255)( 54,254)( 55,253)( 56,252)
( 57,251)( 58,250)( 59,249)( 60,248)( 61,247)( 62,246)( 63,245)( 64,244)
( 65,243)( 66,242)( 67,241)( 68,240)( 69,222)( 70,238)( 71,237)( 72,236)
( 73,235)( 74,234)( 75,233)( 76,232)( 77,231)( 78,230)( 79,229)( 80,228)
( 81,227)( 82,226)( 83,225)( 84,224)( 85,223)( 86,205)( 87,221)( 88,220)
( 89,219)( 90,218)( 91,217)( 92,216)( 93,215)( 94,214)( 95,213)( 96,212)
( 97,211)( 98,210)( 99,209)(100,208)(101,207)(102,206)(103,188)(104,204)
(105,203)(106,202)(107,201)(108,200)(109,199)(110,198)(111,197)(112,196)
(113,195)(114,194)(115,193)(116,192)(117,191)(118,190)(119,189)(120,171)
(121,187)(122,186)(123,185)(124,184)(125,183)(126,182)(127,181)(128,180)
(129,179)(130,178)(131,177)(132,176)(133,175)(134,174)(135,173)(136,172)
(137,154)(138,170)(139,169)(140,168)(141,167)(142,166)(143,165)(144,164)
(145,163)(146,162)(147,161)(148,160)(149,159)(150,158)(151,157)(152,156)
(153,155);
s1 := Sym(289)!(  1, 19)(  2, 18)(  3, 34)(  4, 33)(  5, 32)(  6, 31)(  7, 30)
(  8, 29)(  9, 28)( 10, 27)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)
( 16, 21)( 17, 20)( 35,274)( 36,273)( 37,289)( 38,288)( 39,287)( 40,286)
( 41,285)( 42,284)( 43,283)( 44,282)( 45,281)( 46,280)( 47,279)( 48,278)
( 49,277)( 50,276)( 51,275)( 52,257)( 53,256)( 54,272)( 55,271)( 56,270)
( 57,269)( 58,268)( 59,267)( 60,266)( 61,265)( 62,264)( 63,263)( 64,262)
( 65,261)( 66,260)( 67,259)( 68,258)( 69,240)( 70,239)( 71,255)( 72,254)
( 73,253)( 74,252)( 75,251)( 76,250)( 77,249)( 78,248)( 79,247)( 80,246)
( 81,245)( 82,244)( 83,243)( 84,242)( 85,241)( 86,223)( 87,222)( 88,238)
( 89,237)( 90,236)( 91,235)( 92,234)( 93,233)( 94,232)( 95,231)( 96,230)
( 97,229)( 98,228)( 99,227)(100,226)(101,225)(102,224)(103,206)(104,205)
(105,221)(106,220)(107,219)(108,218)(109,217)(110,216)(111,215)(112,214)
(113,213)(114,212)(115,211)(116,210)(117,209)(118,208)(119,207)(120,189)
(121,188)(122,204)(123,203)(124,202)(125,201)(126,200)(127,199)(128,198)
(129,197)(130,196)(131,195)(132,194)(133,193)(134,192)(135,191)(136,190)
(137,172)(138,171)(139,187)(140,186)(141,185)(142,184)(143,183)(144,182)
(145,181)(146,180)(147,179)(148,178)(149,177)(150,176)(151,175)(152,174)
(153,173)(154,155)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)
(162,164);
s2 := Sym(289)!(  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)
(  9, 10)( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)
( 26, 27)( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)
( 43, 44)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 60, 61)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)
( 77, 78)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)
( 94, 95)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)
(111,112)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)
(128,129)(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)
(145,146)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163)(172,187)(173,186)(174,185)(175,184)(176,183)(177,182)(178,181)
(179,180)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)
(196,197)(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)
(213,214)(223,238)(224,237)(225,236)(226,235)(227,234)(228,233)(229,232)
(230,231)(240,255)(241,254)(242,253)(243,252)(244,251)(245,250)(246,249)
(247,248)(257,272)(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)
(264,265)(274,289)(275,288)(276,287)(277,286)(278,285)(279,284)(280,283)
(281,282);
poly := sub<Sym(289)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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