Polytope of Type {102,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {102,4}*816b
if this polytope has a name.
Group : SmallGroup(816,195)
Rank : 3
Schlafli Type : {102,4}
Number of vertices, edges, etc : 102, 204, 4
Order of s0s1s2 : 102
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {102,4,2} of size 1632
Vertex Figure Of :
   {2,102,4} of size 1632
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {51,4}*408
   17-fold quotients : {6,4}*48c
   34-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {204,4}*1632b, {204,4}*1632c, {102,4}*1632
Irregular Quotients (of which this is a minimal cover):
   None.

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

Twisty Puzzle