Polytope of Type {102,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {102,8}*1632
Also Known As : {102,8|2}. if this polytope has another name.
Group : SmallGroup(1632,871)
Rank : 3
Schlafli Type : {102,8}
Number of vertices, edges, etc : 102, 408, 8
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 : {102,4}*816a
   3-fold quotients : {34,8}*544
   4-fold quotients : {102,2}*408
   6-fold quotients : {34,4}*272
   8-fold quotients : {51,2}*204
   12-fold quotients : {34,2}*136
   17-fold quotients : {6,8}*96
   24-fold quotients : {17,2}*68
   34-fold quotients : {6,4}*48a
   51-fold quotients : {2,8}*32
   68-fold quotients : {6,2}*24
   102-fold quotients : {2,4}*16
   136-fold quotients : {3,2}*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)( 18, 35)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 46)( 25, 45)( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 39)( 32, 38)( 33, 37)( 34, 36)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)( 60, 61)( 69, 86)( 70,102)( 71,101)( 72,100)( 73, 99)( 74, 98)( 75, 97)( 76, 96)( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81, 91)( 82, 90)( 83, 89)( 84, 88)( 85, 87)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(120,137)(121,153)(122,152)(123,151)(124,150)(125,149)(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)(132,142)(133,141)(134,140)(135,139)(136,138)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)(171,188)(172,204)(173,203)(174,202)(175,201)(176,200)(177,199)(178,198)(179,197)(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189)(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)(213,214)(222,239)(223,255)(224,254)(225,253)(226,252)(227,251)(228,250)(229,249)(230,248)(231,247)(232,246)(233,245)(234,244)(235,243)(236,242)(237,241)(238,240)(257,272)(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)(264,265)(273,290)(274,306)(275,305)(276,304)(277,303)(278,302)(279,301)(280,300)(281,299)(282,298)(283,297)(284,296)(285,295)(286,294)(287,293)(288,292)(289,291)(308,323)(309,322)(310,321)(311,320)(312,319)(313,318)(314,317)(315,316)(324,341)(325,357)(326,356)(327,355)(328,354)(329,353)(330,352)(331,351)(332,350)(333,349)(334,348)(335,347)(336,346)(337,345)(338,344)(339,343)(340,342)(359,374)(360,373)(361,372)(362,371)(363,370)(364,369)(365,368)(366,367)(375,392)(376,408)(377,407)(378,406)(379,405)(380,404)(381,403)(382,402)(383,401)(384,400)(385,399)(386,398)(387,397)(388,396)(389,395)(390,394)(391,393);;
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, 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)(103,172)(104,171)(105,187)(106,186)(107,185)(108,184)(109,183)(110,182)(111,181)(112,180)(113,179)(114,178)(115,177)(116,176)(117,175)(118,174)(119,173)(120,155)(121,154)(122,170)(123,169)(124,168)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157)(136,156)(137,189)(138,188)(139,204)(140,203)(141,202)(142,201)(143,200)(144,199)(145,198)(146,197)(147,196)(148,195)(149,194)(150,193)(151,192)(152,191)(153,190)(205,325)(206,324)(207,340)(208,339)(209,338)(210,337)(211,336)(212,335)(213,334)(214,333)(215,332)(216,331)(217,330)(218,329)(219,328)(220,327)(221,326)(222,308)(223,307)(224,323)(225,322)(226,321)(227,320)(228,319)(229,318)(230,317)(231,316)(232,315)(233,314)(234,313)(235,312)(236,311)(237,310)(238,309)(239,342)(240,341)(241,357)(242,356)(243,355)(244,354)(245,353)(246,352)(247,351)(248,350)(249,349)(250,348)(251,347)(252,346)(253,345)(254,344)(255,343)(256,376)(257,375)(258,391)(259,390)(260,389)(261,388)(262,387)(263,386)(264,385)(265,384)(266,383)(267,382)(268,381)(269,380)(270,379)(271,378)(272,377)(273,359)(274,358)(275,374)(276,373)(277,372)(278,371)(279,370)(280,369)(281,368)(282,367)(283,366)(284,365)(285,364)(286,363)(287,362)(288,361)(289,360)(290,393)(291,392)(292,408)(293,407)(294,406)(295,405)(296,404)(297,403)(298,402)(299,401)(300,400)(301,399)(302,398)(303,397)(304,396)(305,395)(306,394);;
s2 := (  1,205)(  2,206)(  3,207)(  4,208)(  5,209)(  6,210)(  7,211)(  8,212)(  9,213)( 10,214)( 11,215)( 12,216)( 13,217)( 14,218)( 15,219)( 16,220)( 17,221)( 18,222)( 19,223)( 20,224)( 21,225)( 22,226)( 23,227)( 24,228)( 25,229)( 26,230)( 27,231)( 28,232)( 29,233)( 30,234)( 31,235)( 32,236)( 33,237)( 34,238)( 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)( 52,256)( 53,257)( 54,258)( 55,259)( 56,260)( 57,261)( 58,262)( 59,263)( 60,264)( 61,265)( 62,266)( 63,267)( 64,268)( 65,269)( 66,270)( 67,271)( 68,272)( 69,273)( 70,274)( 71,275)( 72,276)( 73,277)( 74,278)( 75,279)( 76,280)( 77,281)( 78,282)( 79,283)( 80,284)( 81,285)( 82,286)( 83,287)( 84,288)( 85,289)( 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)(103,358)(104,359)(105,360)(106,361)(107,362)(108,363)(109,364)(110,365)(111,366)(112,367)(113,368)(114,369)(115,370)(116,371)(117,372)(118,373)(119,374)(120,375)(121,376)(122,377)(123,378)(124,379)(125,380)(126,381)(127,382)(128,383)(129,384)(130,385)(131,386)(132,387)(133,388)(134,389)(135,390)(136,391)(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)(154,307)(155,308)(156,309)(157,310)(158,311)(159,312)(160,313)(161,314)(162,315)(163,316)(164,317)(165,318)(166,319)(167,320)(168,321)(169,322)(170,323)(171,324)(172,325)(173,326)(174,327)(175,328)(176,329)(177,330)(178,331)(179,332)(180,333)(181,334)(182,335)(183,336)(184,337)(185,338)(186,339)(187,340)(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, 
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*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*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)( 18, 35)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 46)( 25, 45)( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 39)( 32, 38)( 33, 37)( 34, 36)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)( 60, 61)( 69, 86)( 70,102)( 71,101)( 72,100)( 73, 99)( 74, 98)( 75, 97)( 76, 96)( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81, 91)( 82, 90)( 83, 89)( 84, 88)( 85, 87)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(120,137)(121,153)(122,152)(123,151)(124,150)(125,149)(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)(132,142)(133,141)(134,140)(135,139)(136,138)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)(171,188)(172,204)(173,203)(174,202)(175,201)(176,200)(177,199)(178,198)(179,197)(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189)(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)(213,214)(222,239)(223,255)(224,254)(225,253)(226,252)(227,251)(228,250)(229,249)(230,248)(231,247)(232,246)(233,245)(234,244)(235,243)(236,242)(237,241)(238,240)(257,272)(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)(264,265)(273,290)(274,306)(275,305)(276,304)(277,303)(278,302)(279,301)(280,300)(281,299)(282,298)(283,297)(284,296)(285,295)(286,294)(287,293)(288,292)(289,291)(308,323)(309,322)(310,321)(311,320)(312,319)(313,318)(314,317)(315,316)(324,341)(325,357)(326,356)(327,355)(328,354)(329,353)(330,352)(331,351)(332,350)(333,349)(334,348)(335,347)(336,346)(337,345)(338,344)(339,343)(340,342)(359,374)(360,373)(361,372)(362,371)(363,370)(364,369)(365,368)(366,367)(375,392)(376,408)(377,407)(378,406)(379,405)(380,404)(381,403)(382,402)(383,401)(384,400)(385,399)(386,398)(387,397)(388,396)(389,395)(390,394)(391,393);
s1 := 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)(103,172)(104,171)(105,187)(106,186)(107,185)(108,184)(109,183)(110,182)(111,181)(112,180)(113,179)(114,178)(115,177)(116,176)(117,175)(118,174)(119,173)(120,155)(121,154)(122,170)(123,169)(124,168)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157)(136,156)(137,189)(138,188)(139,204)(140,203)(141,202)(142,201)(143,200)(144,199)(145,198)(146,197)(147,196)(148,195)(149,194)(150,193)(151,192)(152,191)(153,190)(205,325)(206,324)(207,340)(208,339)(209,338)(210,337)(211,336)(212,335)(213,334)(214,333)(215,332)(216,331)(217,330)(218,329)(219,328)(220,327)(221,326)(222,308)(223,307)(224,323)(225,322)(226,321)(227,320)(228,319)(229,318)(230,317)(231,316)(232,315)(233,314)(234,313)(235,312)(236,311)(237,310)(238,309)(239,342)(240,341)(241,357)(242,356)(243,355)(244,354)(245,353)(246,352)(247,351)(248,350)(249,349)(250,348)(251,347)(252,346)(253,345)(254,344)(255,343)(256,376)(257,375)(258,391)(259,390)(260,389)(261,388)(262,387)(263,386)(264,385)(265,384)(266,383)(267,382)(268,381)(269,380)(270,379)(271,378)(272,377)(273,359)(274,358)(275,374)(276,373)(277,372)(278,371)(279,370)(280,369)(281,368)(282,367)(283,366)(284,365)(285,364)(286,363)(287,362)(288,361)(289,360)(290,393)(291,392)(292,408)(293,407)(294,406)(295,405)(296,404)(297,403)(298,402)(299,401)(300,400)(301,399)(302,398)(303,397)(304,396)(305,395)(306,394);
s2 := Sym(408)!(  1,205)(  2,206)(  3,207)(  4,208)(  5,209)(  6,210)(  7,211)(  8,212)(  9,213)( 10,214)( 11,215)( 12,216)( 13,217)( 14,218)( 15,219)( 16,220)( 17,221)( 18,222)( 19,223)( 20,224)( 21,225)( 22,226)( 23,227)( 24,228)( 25,229)( 26,230)( 27,231)( 28,232)( 29,233)( 30,234)( 31,235)( 32,236)( 33,237)( 34,238)( 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)( 52,256)( 53,257)( 54,258)( 55,259)( 56,260)( 57,261)( 58,262)( 59,263)( 60,264)( 61,265)( 62,266)( 63,267)( 64,268)( 65,269)( 66,270)( 67,271)( 68,272)( 69,273)( 70,274)( 71,275)( 72,276)( 73,277)( 74,278)( 75,279)( 76,280)( 77,281)( 78,282)( 79,283)( 80,284)( 81,285)( 82,286)( 83,287)( 84,288)( 85,289)( 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)(103,358)(104,359)(105,360)(106,361)(107,362)(108,363)(109,364)(110,365)(111,366)(112,367)(113,368)(114,369)(115,370)(116,371)(117,372)(118,373)(119,374)(120,375)(121,376)(122,377)(123,378)(124,379)(125,380)(126,381)(127,382)(128,383)(129,384)(130,385)(131,386)(132,387)(133,388)(134,389)(135,390)(136,391)(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)(154,307)(155,308)(156,309)(157,310)(158,311)(159,312)(160,313)(161,314)(162,315)(163,316)(164,317)(165,318)(166,319)(167,320)(168,321)(169,322)(170,323)(171,324)(172,325)(173,326)(174,327)(175,328)(176,329)(177,330)(178,331)(179,332)(180,333)(181,334)(182,335)(183,336)(184,337)(185,338)(186,339)(187,340)(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, 
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*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*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