Polytope of Type {4,204}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,204}*1632a
Also Known As : {4,204|2}. if this polytope has another name.
Group : SmallGroup(1632,844)
Rank : 3
Schlafli Type : {4,204}
Number of vertices, edges, etc : 4, 408, 204
Order of s0s1s2 : 204
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 : {2,204}*816, {4,102}*816a
   3-fold quotients : {4,68}*544
   4-fold quotients : {2,102}*408
   6-fold quotients : {2,68}*272, {4,34}*272
   8-fold quotients : {2,51}*204
   12-fold quotients : {2,34}*136
   17-fold quotients : {4,12}*96a
   24-fold quotients : {2,17}*68
   34-fold quotients : {2,12}*48, {4,6}*48a
   51-fold quotients : {4,4}*32
   68-fold quotients : {2,6}*24
   102-fold quotients : {2,4}*16, {4,2}*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 := (205,307)(206,308)(207,309)(208,310)(209,311)(210,312)(211,313)(212,314)(213,315)(214,316)(215,317)(216,318)(217,319)(218,320)(219,321)(220,322)(221,323)(222,324)(223,325)(224,326)(225,327)(226,328)(227,329)(228,330)(229,331)(230,332)(231,333)(232,334)(233,335)(234,336)(235,337)(236,338)(237,339)(238,340)(239,341)(240,342)(241,343)(242,344)(243,345)(244,346)(245,347)(246,348)(247,349)(248,350)(249,351)(250,352)(251,353)(252,354)(253,355)(254,356)(255,357)(256,358)(257,359)(258,360)(259,361)(260,362)(261,363)(262,364)(263,365)(264,366)(265,367)(266,368)(267,369)(268,370)(269,371)(270,372)(271,373)(272,374)(273,375)(274,376)(275,377)(276,378)(277,379)(278,380)(279,381)(280,382)(281,383)(282,384)(283,385)(284,386)(285,387)(286,388)(287,389)(288,390)(289,391)(290,392)(291,393)(292,394)(293,395)(294,396)(295,397)(296,398)(297,399)(298,400)(299,401)(300,402)(301,403)(302,404)(303,405)(304,406)(305,407)(306,408);;
s1 := (  1,205)(  2,221)(  3,220)(  4,219)(  5,218)(  6,217)(  7,216)(  8,215)(  9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,209)( 15,208)( 16,207)( 17,206)( 18,239)( 19,255)( 20,254)( 21,253)( 22,252)( 23,251)( 24,250)( 25,249)( 26,248)( 27,247)( 28,246)( 29,245)( 30,244)( 31,243)( 32,242)( 33,241)( 34,240)( 35,222)( 36,238)( 37,237)( 38,236)( 39,235)( 40,234)( 41,233)( 42,232)( 43,231)( 44,230)( 45,229)( 46,228)( 47,227)( 48,226)( 49,225)( 50,224)( 51,223)( 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)( 69,290)( 70,306)( 71,305)( 72,304)( 73,303)( 74,302)( 75,301)( 76,300)( 77,299)( 78,298)( 79,297)( 80,296)( 81,295)( 82,294)( 83,293)( 84,292)( 85,291)( 86,273)( 87,289)( 88,288)( 89,287)( 90,286)( 91,285)( 92,284)( 93,283)( 94,282)( 95,281)( 96,280)( 97,279)( 98,278)( 99,277)(100,276)(101,275)(102,274)(103,307)(104,323)(105,322)(106,321)(107,320)(108,319)(109,318)(110,317)(111,316)(112,315)(113,314)(114,313)(115,312)(116,311)(117,310)(118,309)(119,308)(120,341)(121,357)(122,356)(123,355)(124,354)(125,353)(126,352)(127,351)(128,350)(129,349)(130,348)(131,347)(132,346)(133,345)(134,344)(135,343)(136,342)(137,324)(138,340)(139,339)(140,338)(141,337)(142,336)(143,335)(144,334)(145,333)(146,332)(147,331)(148,330)(149,329)(150,328)(151,327)(152,326)(153,325)(154,358)(155,374)(156,373)(157,372)(158,371)(159,370)(160,369)(161,368)(162,367)(163,366)(164,365)(165,364)(166,363)(167,362)(168,361)(169,360)(170,359)(171,392)(172,408)(173,407)(174,406)(175,405)(176,404)(177,403)(178,402)(179,401)(180,400)(181,399)(182,398)(183,397)(184,396)(185,395)(186,394)(187,393)(188,375)(189,391)(190,390)(191,389)(192,388)(193,387)(194,386)(195,385)(196,384)(197,383)(198,382)(199,381)(200,380)(201,379)(202,378)(203,377)(204,376);;
s2 := (  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, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)( 52, 70)( 53, 69)( 54, 85)( 55, 84)( 56, 83)( 57, 82)( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(103,121)(104,120)(105,136)(106,135)(107,134)(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)(116,125)(117,124)(118,123)(119,122)(137,138)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)(154,172)(155,171)(156,187)(157,186)(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(169,174)(170,173)(188,189)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)(205,274)(206,273)(207,289)(208,288)(209,287)(210,286)(211,285)(212,284)(213,283)(214,282)(215,281)(216,280)(217,279)(218,278)(219,277)(220,276)(221,275)(222,257)(223,256)(224,272)(225,271)(226,270)(227,269)(228,268)(229,267)(230,266)(231,265)(232,264)(233,263)(234,262)(235,261)(236,260)(237,259)(238,258)(239,291)(240,290)(241,306)(242,305)(243,304)(244,303)(245,302)(246,301)(247,300)(248,299)(249,298)(250,297)(251,296)(252,295)(253,294)(254,293)(255,292)(307,376)(308,375)(309,391)(310,390)(311,389)(312,388)(313,387)(314,386)(315,385)(316,384)(317,383)(318,382)(319,381)(320,380)(321,379)(322,378)(323,377)(324,359)(325,358)(326,374)(327,373)(328,372)(329,371)(330,370)(331,369)(332,368)(333,367)(334,366)(335,365)(336,364)(337,363)(338,362)(339,361)(340,360)(341,393)(342,392)(343,408)(344,407)(345,406)(346,405)(347,404)(348,403)(349,402)(350,401)(351,400)(352,399)(353,398)(354,397)(355,396)(356,395)(357,394);;
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*s0*s1*s0*s1*s0*s1, 
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*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*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*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*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*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*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(408)!(205,307)(206,308)(207,309)(208,310)(209,311)(210,312)(211,313)(212,314)(213,315)(214,316)(215,317)(216,318)(217,319)(218,320)(219,321)(220,322)(221,323)(222,324)(223,325)(224,326)(225,327)(226,328)(227,329)(228,330)(229,331)(230,332)(231,333)(232,334)(233,335)(234,336)(235,337)(236,338)(237,339)(238,340)(239,341)(240,342)(241,343)(242,344)(243,345)(244,346)(245,347)(246,348)(247,349)(248,350)(249,351)(250,352)(251,353)(252,354)(253,355)(254,356)(255,357)(256,358)(257,359)(258,360)(259,361)(260,362)(261,363)(262,364)(263,365)(264,366)(265,367)(266,368)(267,369)(268,370)(269,371)(270,372)(271,373)(272,374)(273,375)(274,376)(275,377)(276,378)(277,379)(278,380)(279,381)(280,382)(281,383)(282,384)(283,385)(284,386)(285,387)(286,388)(287,389)(288,390)(289,391)(290,392)(291,393)(292,394)(293,395)(294,396)(295,397)(296,398)(297,399)(298,400)(299,401)(300,402)(301,403)(302,404)(303,405)(304,406)(305,407)(306,408);
s1 := Sym(408)!(  1,205)(  2,221)(  3,220)(  4,219)(  5,218)(  6,217)(  7,216)(  8,215)(  9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,209)( 15,208)( 16,207)( 17,206)( 18,239)( 19,255)( 20,254)( 21,253)( 22,252)( 23,251)( 24,250)( 25,249)( 26,248)( 27,247)( 28,246)( 29,245)( 30,244)( 31,243)( 32,242)( 33,241)( 34,240)( 35,222)( 36,238)( 37,237)( 38,236)( 39,235)( 40,234)( 41,233)( 42,232)( 43,231)( 44,230)( 45,229)( 46,228)( 47,227)( 48,226)( 49,225)( 50,224)( 51,223)( 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)( 69,290)( 70,306)( 71,305)( 72,304)( 73,303)( 74,302)( 75,301)( 76,300)( 77,299)( 78,298)( 79,297)( 80,296)( 81,295)( 82,294)( 83,293)( 84,292)( 85,291)( 86,273)( 87,289)( 88,288)( 89,287)( 90,286)( 91,285)( 92,284)( 93,283)( 94,282)( 95,281)( 96,280)( 97,279)( 98,278)( 99,277)(100,276)(101,275)(102,274)(103,307)(104,323)(105,322)(106,321)(107,320)(108,319)(109,318)(110,317)(111,316)(112,315)(113,314)(114,313)(115,312)(116,311)(117,310)(118,309)(119,308)(120,341)(121,357)(122,356)(123,355)(124,354)(125,353)(126,352)(127,351)(128,350)(129,349)(130,348)(131,347)(132,346)(133,345)(134,344)(135,343)(136,342)(137,324)(138,340)(139,339)(140,338)(141,337)(142,336)(143,335)(144,334)(145,333)(146,332)(147,331)(148,330)(149,329)(150,328)(151,327)(152,326)(153,325)(154,358)(155,374)(156,373)(157,372)(158,371)(159,370)(160,369)(161,368)(162,367)(163,366)(164,365)(165,364)(166,363)(167,362)(168,361)(169,360)(170,359)(171,392)(172,408)(173,407)(174,406)(175,405)(176,404)(177,403)(178,402)(179,401)(180,400)(181,399)(182,398)(183,397)(184,396)(185,395)(186,394)(187,393)(188,375)(189,391)(190,390)(191,389)(192,388)(193,387)(194,386)(195,385)(196,384)(197,383)(198,382)(199,381)(200,380)(201,379)(202,378)(203,377)(204,376);
s2 := Sym(408)!(  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, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)( 52, 70)( 53, 69)( 54, 85)( 55, 84)( 56, 83)( 57, 82)( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(103,121)(104,120)(105,136)(106,135)(107,134)(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)(116,125)(117,124)(118,123)(119,122)(137,138)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)(154,172)(155,171)(156,187)(157,186)(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(169,174)(170,173)(188,189)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)(205,274)(206,273)(207,289)(208,288)(209,287)(210,286)(211,285)(212,284)(213,283)(214,282)(215,281)(216,280)(217,279)(218,278)(219,277)(220,276)(221,275)(222,257)(223,256)(224,272)(225,271)(226,270)(227,269)(228,268)(229,267)(230,266)(231,265)(232,264)(233,263)(234,262)(235,261)(236,260)(237,259)(238,258)(239,291)(240,290)(241,306)(242,305)(243,304)(244,303)(245,302)(246,301)(247,300)(248,299)(249,298)(250,297)(251,296)(252,295)(253,294)(254,293)(255,292)(307,376)(308,375)(309,391)(310,390)(311,389)(312,388)(313,387)(314,386)(315,385)(316,384)(317,383)(318,382)(319,381)(320,380)(321,379)(322,378)(323,377)(324,359)(325,358)(326,374)(327,373)(328,372)(329,371)(330,370)(331,369)(332,368)(333,367)(334,366)(335,365)(336,364)(337,363)(338,362)(339,361)(340,360)(341,393)(342,392)(343,408)(344,407)(345,406)(346,405)(347,404)(348,403)(349,402)(350,401)(351,400)(352,399)(353,398)(354,397)(355,396)(356,395)(357,394);
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*s0*s1*s0*s1*s0*s1, 
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*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*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*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*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*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*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