Polytope of Type {34,17}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,17}*1156
if this polytope has a name.
Group : SmallGroup(1156,13)
Rank : 3
Schlafli Type : {34,17}
Number of vertices, edges, etc : 34, 289, 17
Order of s₀s₁s₂ : 34
Order of s₀s₁s₂s₁ : 34
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   17-fold quotients : {2,17}*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)
( 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);;
s1 := (  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)
( 18,274)( 19,273)( 20,289)( 21,288)( 22,287)( 23,286)( 24,285)( 25,284)
( 26,283)( 27,282)( 28,281)( 29,280)( 30,279)( 31,278)( 32,277)( 33,276)
( 34,275)( 35,257)( 36,256)( 37,272)( 38,271)( 39,270)( 40,269)( 41,268)
( 42,267)( 43,266)( 44,265)( 45,264)( 46,263)( 47,262)( 48,261)( 49,260)
( 50,259)( 51,258)( 52,240)( 53,239)( 54,255)( 55,254)( 56,253)( 57,252)
( 58,251)( 59,250)( 60,249)( 61,248)( 62,247)( 63,246)( 64,245)( 65,244)
( 66,243)( 67,242)( 68,241)( 69,223)( 70,222)( 71,238)( 72,237)( 73,236)
( 74,235)( 75,234)( 76,233)( 77,232)( 78,231)( 79,230)( 80,229)( 81,228)
( 82,227)( 83,226)( 84,225)( 85,224)( 86,206)( 87,205)( 88,221)( 89,220)
( 90,219)( 91,218)( 92,217)( 93,216)( 94,215)( 95,214)( 96,213)( 97,212)
( 98,211)( 99,210)(100,209)(101,208)(102,207)(103,189)(104,188)(105,204)
(106,203)(107,202)(108,201)(109,200)(110,199)(111,198)(112,197)(113,196)
(114,195)(115,194)(116,193)(117,192)(118,191)(119,190)(120,172)(121,171)
(122,187)(123,186)(124,185)(125,184)(126,183)(127,182)(128,181)(129,180)
(130,179)(131,178)(132,177)(133,176)(134,175)(135,174)(136,173)(137,155)
(138,154)(139,170)(140,169)(141,168)(142,167)(143,166)(144,165)(145,164)
(146,163)(147,162)(148,161)(149,160)(150,159)(151,158)(152,157)(153,156);;
s2 := (  1, 18)(  2, 34)(  3, 33)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 28)
(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)
( 17, 19)( 35,273)( 36,289)( 37,288)( 38,287)( 39,286)( 40,285)( 41,284)
( 42,283)( 43,282)( 44,281)( 45,280)( 46,279)( 47,278)( 48,277)( 49,276)
( 50,275)( 51,274)( 52,256)( 53,272)( 54,271)( 55,270)( 56,269)( 57,268)
( 58,267)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)( 64,261)( 65,260)
( 66,259)( 67,258)( 68,257)( 69,239)( 70,255)( 71,254)( 72,253)( 73,252)
( 74,251)( 75,250)( 76,249)( 77,248)( 78,247)( 79,246)( 80,245)( 81,244)
( 82,243)( 83,242)( 84,241)( 85,240)( 86,222)( 87,238)( 88,237)( 89,236)
( 90,235)( 91,234)( 92,233)( 93,232)( 94,231)( 95,230)( 96,229)( 97,228)
( 98,227)( 99,226)(100,225)(101,224)(102,223)(103,205)(104,221)(105,220)
(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)(112,213)(113,212)
(114,211)(115,210)(116,209)(117,208)(118,207)(119,206)(120,188)(121,204)
(122,203)(123,202)(124,201)(125,200)(126,199)(127,198)(128,197)(129,196)
(130,195)(131,194)(132,193)(133,192)(134,191)(135,190)(136,189)(137,171)
(138,187)(139,186)(140,185)(141,184)(142,183)(143,182)(144,181)(145,180)
(146,179)(147,178)(148,177)(149,176)(150,175)(151,174)(152,173)(153,172)
(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163);;
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*s0*s1*s2*s0*s1*s0*s1, 
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(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);
s1 := Sym(289)!(  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)
(  9, 11)( 18,274)( 19,273)( 20,289)( 21,288)( 22,287)( 23,286)( 24,285)
( 25,284)( 26,283)( 27,282)( 28,281)( 29,280)( 30,279)( 31,278)( 32,277)
( 33,276)( 34,275)( 35,257)( 36,256)( 37,272)( 38,271)( 39,270)( 40,269)
( 41,268)( 42,267)( 43,266)( 44,265)( 45,264)( 46,263)( 47,262)( 48,261)
( 49,260)( 50,259)( 51,258)( 52,240)( 53,239)( 54,255)( 55,254)( 56,253)
( 57,252)( 58,251)( 59,250)( 60,249)( 61,248)( 62,247)( 63,246)( 64,245)
( 65,244)( 66,243)( 67,242)( 68,241)( 69,223)( 70,222)( 71,238)( 72,237)
( 73,236)( 74,235)( 75,234)( 76,233)( 77,232)( 78,231)( 79,230)( 80,229)
( 81,228)( 82,227)( 83,226)( 84,225)( 85,224)( 86,206)( 87,205)( 88,221)
( 89,220)( 90,219)( 91,218)( 92,217)( 93,216)( 94,215)( 95,214)( 96,213)
( 97,212)( 98,211)( 99,210)(100,209)(101,208)(102,207)(103,189)(104,188)
(105,204)(106,203)(107,202)(108,201)(109,200)(110,199)(111,198)(112,197)
(113,196)(114,195)(115,194)(116,193)(117,192)(118,191)(119,190)(120,172)
(121,171)(122,187)(123,186)(124,185)(125,184)(126,183)(127,182)(128,181)
(129,180)(130,179)(131,178)(132,177)(133,176)(134,175)(135,174)(136,173)
(137,155)(138,154)(139,170)(140,169)(141,168)(142,167)(143,166)(144,165)
(145,164)(146,163)(147,162)(148,161)(149,160)(150,159)(151,158)(152,157)
(153,156);
s2 := Sym(289)!(  1, 18)(  2, 34)(  3, 33)(  4, 32)(  5, 31)(  6, 30)(  7, 29)
(  8, 28)(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 35,273)( 36,289)( 37,288)( 38,287)( 39,286)( 40,285)
( 41,284)( 42,283)( 43,282)( 44,281)( 45,280)( 46,279)( 47,278)( 48,277)
( 49,276)( 50,275)( 51,274)( 52,256)( 53,272)( 54,271)( 55,270)( 56,269)
( 57,268)( 58,267)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)( 64,261)
( 65,260)( 66,259)( 67,258)( 68,257)( 69,239)( 70,255)( 71,254)( 72,253)
( 73,252)( 74,251)( 75,250)( 76,249)( 77,248)( 78,247)( 79,246)( 80,245)
( 81,244)( 82,243)( 83,242)( 84,241)( 85,240)( 86,222)( 87,238)( 88,237)
( 89,236)( 90,235)( 91,234)( 92,233)( 93,232)( 94,231)( 95,230)( 96,229)
( 97,228)( 98,227)( 99,226)(100,225)(101,224)(102,223)(103,205)(104,221)
(105,220)(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)(112,213)
(113,212)(114,211)(115,210)(116,209)(117,208)(118,207)(119,206)(120,188)
(121,204)(122,203)(123,202)(124,201)(125,200)(126,199)(127,198)(128,197)
(129,196)(130,195)(131,194)(132,193)(133,192)(134,191)(135,190)(136,189)
(137,171)(138,187)(139,186)(140,185)(141,184)(142,183)(143,182)(144,181)
(145,180)(146,179)(147,178)(148,177)(149,176)(150,175)(151,174)(152,173)
(153,172)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163);
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*s0*s1*s2*s0*s1*s0*s1, 
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 >;

References : None.
to this polytope