Part of the Atlas of Small Regular Polytopes

Polytope of Type {34,17}

Atlas Canonical Name {34,17}*1156

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1156,13)
Rank
3
Schläfli Type
{34,17}
Vertices, edges, …
34, 289, 17
Order of s0s1s2
34
Order of s0s1s2s1
34
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat
  • Self-Petrie

Quotients maximal quotients in bold

17-fold

Covers minimal covers in bold

None in this atlas.

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)( 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, s0*s1*s2*s0*s1*s0*s1*s2*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, s0*s1*s2*s0*s1*s0*s1*s2*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.

Twisty Puzzle