Polytope of Type {34,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,24}*1632
Also Known As : {34,24|2}. if this polytope has another name.
Group : SmallGroup(1632,320)
Rank : 3
Schlafli Type : {34,24}
Number of vertices, edges, etc : 34, 408, 24
Order of s0s1s2 : 408
Order of s0s1s2s1 : 2
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) :
   2-fold quotients : {34,12}*816
   3-fold quotients : {34,8}*544
   4-fold quotients : {34,6}*408
   6-fold quotients : {34,4}*272
   12-fold quotients : {34,2}*136
   17-fold quotients : {2,24}*96
   24-fold quotients : {17,2}*68
   34-fold quotients : {2,12}*48
   51-fold quotients : {2,8}*32
   68-fold quotients : {2,6}*24
   102-fold quotients : {2,4}*16
   136-fold quotients : {2,3}*12
   204-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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)(291,306)(292,305)(293,304)(294,303)(295,302)(296,301)(297,300)(298,299)(308,323)(309,322)(310,321)(311,320)(312,319)(313,318)(314,317)(315,316)(325,340)(326,339)(327,338)(328,337)(329,336)(330,335)(331,334)(332,333)(342,357)(343,356)(344,355)(345,354)(346,353)(347,352)(348,351)(349,350)(359,374)(360,373)(361,372)(362,371)(363,370)(364,369)(365,368)(366,367)(376,391)(377,390)(378,389)(379,388)(380,387)(381,386)(382,385)(383,384)(393,408)(394,407)(395,406)(396,405)(397,404)(398,403)(399,402)(400,401);;
s1 := (  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 18, 36)( 19, 35)( 20, 51)( 21, 50)( 22, 49)( 23, 48)( 24, 47)( 25, 46)( 26, 45)( 27, 44)( 28, 43)( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)( 60, 62)( 69, 87)( 70, 86)( 71,102)( 72,101)( 73,100)( 74, 99)( 75, 98)( 76, 97)( 77, 96)( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)(103,155)(104,154)(105,170)(106,169)(107,168)(108,167)(109,166)(110,165)(111,164)(112,163)(113,162)(114,161)(115,160)(116,159)(117,158)(118,157)(119,156)(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)(205,308)(206,307)(207,323)(208,322)(209,321)(210,320)(211,319)(212,318)(213,317)(214,316)(215,315)(216,314)(217,313)(218,312)(219,311)(220,310)(221,309)(222,342)(223,341)(224,357)(225,356)(226,355)(227,354)(228,353)(229,352)(230,351)(231,350)(232,349)(233,348)(234,347)(235,346)(236,345)(237,344)(238,343)(239,325)(240,324)(241,340)(242,339)(243,338)(244,337)(245,336)(246,335)(247,334)(248,333)(249,332)(250,331)(251,330)(252,329)(253,328)(254,327)(255,326)(256,359)(257,358)(258,374)(259,373)(260,372)(261,371)(262,370)(263,369)(264,368)(265,367)(266,366)(267,365)(268,364)(269,363)(270,362)(271,361)(272,360)(273,393)(274,392)(275,408)(276,407)(277,406)(278,405)(279,404)(280,403)(281,402)(282,401)(283,400)(284,399)(285,398)(286,397)(287,396)(288,395)(289,394)(290,376)(291,375)(292,391)(293,390)(294,389)(295,388)(296,387)(297,386)(298,385)(299,384)(300,383)(301,382)(302,381)(303,380)(304,379)(305,378)(306,377);;
s2 := (  1,222)(  2,223)(  3,224)(  4,225)(  5,226)(  6,227)(  7,228)(  8,229)(  9,230)( 10,231)( 11,232)( 12,233)( 13,234)( 14,235)( 15,236)( 16,237)( 17,238)( 18,205)( 19,206)( 20,207)( 21,208)( 22,209)( 23,210)( 24,211)( 25,212)( 26,213)( 27,214)( 28,215)( 29,216)( 30,217)( 31,218)( 32,219)( 33,220)( 34,221)( 35,239)( 36,240)( 37,241)( 38,242)( 39,243)( 40,244)( 41,245)( 42,246)( 43,247)( 44,248)( 45,249)( 46,250)( 47,251)( 48,252)( 49,253)( 50,254)( 51,255)( 52,273)( 53,274)( 54,275)( 55,276)( 56,277)( 57,278)( 58,279)( 59,280)( 60,281)( 61,282)( 62,283)( 63,284)( 64,285)( 65,286)( 66,287)( 67,288)( 68,289)( 69,256)( 70,257)( 71,258)( 72,259)( 73,260)( 74,261)( 75,262)( 76,263)( 77,264)( 78,265)( 79,266)( 80,267)( 81,268)( 82,269)( 83,270)( 84,271)( 85,272)( 86,290)( 87,291)( 88,292)( 89,293)( 90,294)( 91,295)( 92,296)( 93,297)( 94,298)( 95,299)( 96,300)( 97,301)( 98,302)( 99,303)(100,304)(101,305)(102,306)(103,375)(104,376)(105,377)(106,378)(107,379)(108,380)(109,381)(110,382)(111,383)(112,384)(113,385)(114,386)(115,387)(116,388)(117,389)(118,390)(119,391)(120,358)(121,359)(122,360)(123,361)(124,362)(125,363)(126,364)(127,365)(128,366)(129,367)(130,368)(131,369)(132,370)(133,371)(134,372)(135,373)(136,374)(137,392)(138,393)(139,394)(140,395)(141,396)(142,397)(143,398)(144,399)(145,400)(146,401)(147,402)(148,403)(149,404)(150,405)(151,406)(152,407)(153,408)(154,324)(155,325)(156,326)(157,327)(158,328)(159,329)(160,330)(161,331)(162,332)(163,333)(164,334)(165,335)(166,336)(167,337)(168,338)(169,339)(170,340)(171,307)(172,308)(173,309)(174,310)(175,311)(176,312)(177,313)(178,314)(179,315)(180,316)(181,317)(182,318)(183,319)(184,320)(185,321)(186,322)(187,323)(188,341)(189,342)(190,343)(191,344)(192,345)(193,346)(194,347)(195,348)(196,349)(197,350)(198,351)(199,352)(200,353)(201,354)(202,355)(203,356)(204,357);;
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*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(408)!(  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)(291,306)(292,305)(293,304)(294,303)(295,302)(296,301)(297,300)(298,299)(308,323)(309,322)(310,321)(311,320)(312,319)(313,318)(314,317)(315,316)(325,340)(326,339)(327,338)(328,337)(329,336)(330,335)(331,334)(332,333)(342,357)(343,356)(344,355)(345,354)(346,353)(347,352)(348,351)(349,350)(359,374)(360,373)(361,372)(362,371)(363,370)(364,369)(365,368)(366,367)(376,391)(377,390)(378,389)(379,388)(380,387)(381,386)(382,385)(383,384)(393,408)(394,407)(395,406)(396,405)(397,404)(398,403)(399,402)(400,401);
s1 := Sym(408)!(  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 18, 36)( 19, 35)( 20, 51)( 21, 50)( 22, 49)( 23, 48)( 24, 47)( 25, 46)( 26, 45)( 27, 44)( 28, 43)( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)( 60, 62)( 69, 87)( 70, 86)( 71,102)( 72,101)( 73,100)( 74, 99)( 75, 98)( 76, 97)( 77, 96)( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)(103,155)(104,154)(105,170)(106,169)(107,168)(108,167)(109,166)(110,165)(111,164)(112,163)(113,162)(114,161)(115,160)(116,159)(117,158)(118,157)(119,156)(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)(205,308)(206,307)(207,323)(208,322)(209,321)(210,320)(211,319)(212,318)(213,317)(214,316)(215,315)(216,314)(217,313)(218,312)(219,311)(220,310)(221,309)(222,342)(223,341)(224,357)(225,356)(226,355)(227,354)(228,353)(229,352)(230,351)(231,350)(232,349)(233,348)(234,347)(235,346)(236,345)(237,344)(238,343)(239,325)(240,324)(241,340)(242,339)(243,338)(244,337)(245,336)(246,335)(247,334)(248,333)(249,332)(250,331)(251,330)(252,329)(253,328)(254,327)(255,326)(256,359)(257,358)(258,374)(259,373)(260,372)(261,371)(262,370)(263,369)(264,368)(265,367)(266,366)(267,365)(268,364)(269,363)(270,362)(271,361)(272,360)(273,393)(274,392)(275,408)(276,407)(277,406)(278,405)(279,404)(280,403)(281,402)(282,401)(283,400)(284,399)(285,398)(286,397)(287,396)(288,395)(289,394)(290,376)(291,375)(292,391)(293,390)(294,389)(295,388)(296,387)(297,386)(298,385)(299,384)(300,383)(301,382)(302,381)(303,380)(304,379)(305,378)(306,377);
s2 := Sym(408)!(  1,222)(  2,223)(  3,224)(  4,225)(  5,226)(  6,227)(  7,228)(  8,229)(  9,230)( 10,231)( 11,232)( 12,233)( 13,234)( 14,235)( 15,236)( 16,237)( 17,238)( 18,205)( 19,206)( 20,207)( 21,208)( 22,209)( 23,210)( 24,211)( 25,212)( 26,213)( 27,214)( 28,215)( 29,216)( 30,217)( 31,218)( 32,219)( 33,220)( 34,221)( 35,239)( 36,240)( 37,241)( 38,242)( 39,243)( 40,244)( 41,245)( 42,246)( 43,247)( 44,248)( 45,249)( 46,250)( 47,251)( 48,252)( 49,253)( 50,254)( 51,255)( 52,273)( 53,274)( 54,275)( 55,276)( 56,277)( 57,278)( 58,279)( 59,280)( 60,281)( 61,282)( 62,283)( 63,284)( 64,285)( 65,286)( 66,287)( 67,288)( 68,289)( 69,256)( 70,257)( 71,258)( 72,259)( 73,260)( 74,261)( 75,262)( 76,263)( 77,264)( 78,265)( 79,266)( 80,267)( 81,268)( 82,269)( 83,270)( 84,271)( 85,272)( 86,290)( 87,291)( 88,292)( 89,293)( 90,294)( 91,295)( 92,296)( 93,297)( 94,298)( 95,299)( 96,300)( 97,301)( 98,302)( 99,303)(100,304)(101,305)(102,306)(103,375)(104,376)(105,377)(106,378)(107,379)(108,380)(109,381)(110,382)(111,383)(112,384)(113,385)(114,386)(115,387)(116,388)(117,389)(118,390)(119,391)(120,358)(121,359)(122,360)(123,361)(124,362)(125,363)(126,364)(127,365)(128,366)(129,367)(130,368)(131,369)(132,370)(133,371)(134,372)(135,373)(136,374)(137,392)(138,393)(139,394)(140,395)(141,396)(142,397)(143,398)(144,399)(145,400)(146,401)(147,402)(148,403)(149,404)(150,405)(151,406)(152,407)(153,408)(154,324)(155,325)(156,326)(157,327)(158,328)(159,329)(160,330)(161,331)(162,332)(163,333)(164,334)(165,335)(166,336)(167,337)(168,338)(169,339)(170,340)(171,307)(172,308)(173,309)(174,310)(175,311)(176,312)(177,313)(178,314)(179,315)(180,316)(181,317)(182,318)(183,319)(184,320)(185,321)(186,322)(187,323)(188,341)(189,342)(190,343)(191,344)(192,345)(193,346)(194,347)(195,348)(196,349)(197,350)(198,351)(199,352)(200,353)(201,354)(202,355)(203,356)(204,357);
poly := sub<Sym(408)|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*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 >;
References : None.
to this polytope

Twisty Puzzle