Polytope of Type {48,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6}*1728b
if this polytope has a name.
Group : SmallGroup(1728,3073)
Rank : 3
Schlafli Type : {48,6}
Number of vertices, edges, etc : 144, 432, 18
Order of s0s1s2 : 48
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,6}*864b
   3-fold quotients : {48,6}*576a
   4-fold quotients : {12,6}*432b
   6-fold quotients : {24,6}*288a
   8-fold quotients : {6,6}*216b
   9-fold quotients : {48,2}*192, {16,6}*192
   12-fold quotients : {12,6}*144a
   16-fold quotients : {6,6}*108
   18-fold quotients : {24,2}*96, {8,6}*96
   24-fold quotients : {6,6}*72a
   27-fold quotients : {16,2}*64
   36-fold quotients : {12,2}*48, {4,6}*48a
   54-fold quotients : {8,2}*32
   72-fold quotients : {2,6}*24, {6,2}*24
   108-fold quotients : {4,2}*16
   144-fold quotients : {2,3}*12, {3,2}*12
   216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1> of order 3.
      6 facets:
         6 of {48}*96
      80 vertex figures:
         32 of {6}*12
         48 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      10 facets:
         6 of {16}*32
         4 of {48}*96
      48 vertex figures:
         48 of {6}*12

Permutation Representation (GAP) : 
s0 := (  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)( 51, 53)( 55, 82)( 56, 84)( 57, 83)( 58, 88)( 59, 90)( 60, 89)( 61, 85)( 62, 87)( 63, 86)( 64, 91)( 65, 93)( 66, 92)( 67, 97)( 68, 99)( 69, 98)( 70, 94)( 71, 96)( 72, 95)( 73,100)( 74,102)( 75,101)( 76,106)( 77,108)( 78,107)( 79,103)( 80,105)( 81,104)(109,163)(110,165)(111,164)(112,169)(113,171)(114,170)(115,166)(116,168)(117,167)(118,172)(119,174)(120,173)(121,178)(122,180)(123,179)(124,175)(125,177)(126,176)(127,181)(128,183)(129,182)(130,187)(131,189)(132,188)(133,184)(134,186)(135,185)(136,190)(137,192)(138,191)(139,196)(140,198)(141,197)(142,193)(143,195)(144,194)(145,199)(146,201)(147,200)(148,205)(149,207)(150,206)(151,202)(152,204)(153,203)(154,208)(155,210)(156,209)(157,214)(158,216)(159,215)(160,211)(161,213)(162,212)(217,325)(218,327)(219,326)(220,331)(221,333)(222,332)(223,328)(224,330)(225,329)(226,334)(227,336)(228,335)(229,340)(230,342)(231,341)(232,337)(233,339)(234,338)(235,343)(236,345)(237,344)(238,349)(239,351)(240,350)(241,346)(242,348)(243,347)(244,352)(245,354)(246,353)(247,358)(248,360)(249,359)(250,355)(251,357)(252,356)(253,361)(254,363)(255,362)(256,367)(257,369)(258,368)(259,364)(260,366)(261,365)(262,370)(263,372)(264,371)(265,376)(266,378)(267,377)(268,373)(269,375)(270,374)(271,406)(272,408)(273,407)(274,412)(275,414)(276,413)(277,409)(278,411)(279,410)(280,415)(281,417)(282,416)(283,421)(284,423)(285,422)(286,418)(287,420)(288,419)(289,424)(290,426)(291,425)(292,430)(293,432)(294,431)(295,427)(296,429)(297,428)(298,379)(299,381)(300,380)(301,385)(302,387)(303,386)(304,382)(305,384)(306,383)(307,388)(308,390)(309,389)(310,394)(311,396)(312,395)(313,391)(314,393)(315,392)(316,397)(317,399)(318,398)(319,403)(320,405)(321,404)(322,400)(323,402)(324,401);;
s1 := (  1,220)(  2,221)(  3,222)(  4,217)(  5,218)(  6,219)(  7,223)(  8,224)(  9,225)( 10,238)( 11,239)( 12,240)( 13,235)( 14,236)( 15,237)( 16,241)( 17,242)( 18,243)( 19,229)( 20,230)( 21,231)( 22,226)( 23,227)( 24,228)( 25,232)( 26,233)( 27,234)( 28,247)( 29,248)( 30,249)( 31,244)( 32,245)( 33,246)( 34,250)( 35,251)( 36,252)( 37,265)( 38,266)( 39,267)( 40,262)( 41,263)( 42,264)( 43,268)( 44,269)( 45,270)( 46,256)( 47,257)( 48,258)( 49,253)( 50,254)( 51,255)( 52,259)( 53,260)( 54,261)( 55,301)( 56,302)( 57,303)( 58,298)( 59,299)( 60,300)( 61,304)( 62,305)( 63,306)( 64,319)( 65,320)( 66,321)( 67,316)( 68,317)( 69,318)( 70,322)( 71,323)( 72,324)( 73,310)( 74,311)( 75,312)( 76,307)( 77,308)( 78,309)( 79,313)( 80,314)( 81,315)( 82,274)( 83,275)( 84,276)( 85,271)( 86,272)( 87,273)( 88,277)( 89,278)( 90,279)( 91,292)( 92,293)( 93,294)( 94,289)( 95,290)( 96,291)( 97,295)( 98,296)( 99,297)(100,283)(101,284)(102,285)(103,280)(104,281)(105,282)(106,286)(107,287)(108,288)(109,382)(110,383)(111,384)(112,379)(113,380)(114,381)(115,385)(116,386)(117,387)(118,400)(119,401)(120,402)(121,397)(122,398)(123,399)(124,403)(125,404)(126,405)(127,391)(128,392)(129,393)(130,388)(131,389)(132,390)(133,394)(134,395)(135,396)(136,409)(137,410)(138,411)(139,406)(140,407)(141,408)(142,412)(143,413)(144,414)(145,427)(146,428)(147,429)(148,424)(149,425)(150,426)(151,430)(152,431)(153,432)(154,418)(155,419)(156,420)(157,415)(158,416)(159,417)(160,421)(161,422)(162,423)(163,328)(164,329)(165,330)(166,325)(167,326)(168,327)(169,331)(170,332)(171,333)(172,346)(173,347)(174,348)(175,343)(176,344)(177,345)(178,349)(179,350)(180,351)(181,337)(182,338)(183,339)(184,334)(185,335)(186,336)(187,340)(188,341)(189,342)(190,355)(191,356)(192,357)(193,352)(194,353)(195,354)(196,358)(197,359)(198,360)(199,373)(200,374)(201,375)(202,370)(203,371)(204,372)(205,376)(206,377)(207,378)(208,364)(209,365)(210,366)(211,361)(212,362)(213,363)(214,367)(215,368)(216,369);;
s2 := (  1, 10)(  2, 12)(  3, 11)(  4, 14)(  5, 13)(  6, 15)(  7, 18)(  8, 17)(  9, 16)( 20, 21)( 22, 23)( 25, 27)( 28, 37)( 29, 39)( 30, 38)( 31, 41)( 32, 40)( 33, 42)( 34, 45)( 35, 44)( 36, 43)( 47, 48)( 49, 50)( 52, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 68)( 59, 67)( 60, 69)( 61, 72)( 62, 71)( 63, 70)( 74, 75)( 76, 77)( 79, 81)( 82, 91)( 83, 93)( 84, 92)( 85, 95)( 86, 94)( 87, 96)( 88, 99)( 89, 98)( 90, 97)(101,102)(103,104)(106,108)(109,118)(110,120)(111,119)(112,122)(113,121)(114,123)(115,126)(116,125)(117,124)(128,129)(130,131)(133,135)(136,145)(137,147)(138,146)(139,149)(140,148)(141,150)(142,153)(143,152)(144,151)(155,156)(157,158)(160,162)(163,172)(164,174)(165,173)(166,176)(167,175)(168,177)(169,180)(170,179)(171,178)(182,183)(184,185)(187,189)(190,199)(191,201)(192,200)(193,203)(194,202)(195,204)(196,207)(197,206)(198,205)(209,210)(211,212)(214,216)(217,226)(218,228)(219,227)(220,230)(221,229)(222,231)(223,234)(224,233)(225,232)(236,237)(238,239)(241,243)(244,253)(245,255)(246,254)(247,257)(248,256)(249,258)(250,261)(251,260)(252,259)(263,264)(265,266)(268,270)(271,280)(272,282)(273,281)(274,284)(275,283)(276,285)(277,288)(278,287)(279,286)(290,291)(292,293)(295,297)(298,307)(299,309)(300,308)(301,311)(302,310)(303,312)(304,315)(305,314)(306,313)(317,318)(319,320)(322,324)(325,334)(326,336)(327,335)(328,338)(329,337)(330,339)(331,342)(332,341)(333,340)(344,345)(346,347)(349,351)(352,361)(353,363)(354,362)(355,365)(356,364)(357,366)(358,369)(359,368)(360,367)(371,372)(373,374)(376,378)(379,388)(380,390)(381,389)(382,392)(383,391)(384,393)(385,396)(386,395)(387,394)(398,399)(400,401)(403,405)(406,415)(407,417)(408,416)(409,419)(410,418)(411,420)(412,423)(413,422)(414,421)(425,426)(427,428)(430,432);;
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*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(432)!(  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)( 51, 53)( 55, 82)( 56, 84)( 57, 83)( 58, 88)( 59, 90)( 60, 89)( 61, 85)( 62, 87)( 63, 86)( 64, 91)( 65, 93)( 66, 92)( 67, 97)( 68, 99)( 69, 98)( 70, 94)( 71, 96)( 72, 95)( 73,100)( 74,102)( 75,101)( 76,106)( 77,108)( 78,107)( 79,103)( 80,105)( 81,104)(109,163)(110,165)(111,164)(112,169)(113,171)(114,170)(115,166)(116,168)(117,167)(118,172)(119,174)(120,173)(121,178)(122,180)(123,179)(124,175)(125,177)(126,176)(127,181)(128,183)(129,182)(130,187)(131,189)(132,188)(133,184)(134,186)(135,185)(136,190)(137,192)(138,191)(139,196)(140,198)(141,197)(142,193)(143,195)(144,194)(145,199)(146,201)(147,200)(148,205)(149,207)(150,206)(151,202)(152,204)(153,203)(154,208)(155,210)(156,209)(157,214)(158,216)(159,215)(160,211)(161,213)(162,212)(217,325)(218,327)(219,326)(220,331)(221,333)(222,332)(223,328)(224,330)(225,329)(226,334)(227,336)(228,335)(229,340)(230,342)(231,341)(232,337)(233,339)(234,338)(235,343)(236,345)(237,344)(238,349)(239,351)(240,350)(241,346)(242,348)(243,347)(244,352)(245,354)(246,353)(247,358)(248,360)(249,359)(250,355)(251,357)(252,356)(253,361)(254,363)(255,362)(256,367)(257,369)(258,368)(259,364)(260,366)(261,365)(262,370)(263,372)(264,371)(265,376)(266,378)(267,377)(268,373)(269,375)(270,374)(271,406)(272,408)(273,407)(274,412)(275,414)(276,413)(277,409)(278,411)(279,410)(280,415)(281,417)(282,416)(283,421)(284,423)(285,422)(286,418)(287,420)(288,419)(289,424)(290,426)(291,425)(292,430)(293,432)(294,431)(295,427)(296,429)(297,428)(298,379)(299,381)(300,380)(301,385)(302,387)(303,386)(304,382)(305,384)(306,383)(307,388)(308,390)(309,389)(310,394)(311,396)(312,395)(313,391)(314,393)(315,392)(316,397)(317,399)(318,398)(319,403)(320,405)(321,404)(322,400)(323,402)(324,401);
s1 := Sym(432)!(  1,220)(  2,221)(  3,222)(  4,217)(  5,218)(  6,219)(  7,223)(  8,224)(  9,225)( 10,238)( 11,239)( 12,240)( 13,235)( 14,236)( 15,237)( 16,241)( 17,242)( 18,243)( 19,229)( 20,230)( 21,231)( 22,226)( 23,227)( 24,228)( 25,232)( 26,233)( 27,234)( 28,247)( 29,248)( 30,249)( 31,244)( 32,245)( 33,246)( 34,250)( 35,251)( 36,252)( 37,265)( 38,266)( 39,267)( 40,262)( 41,263)( 42,264)( 43,268)( 44,269)( 45,270)( 46,256)( 47,257)( 48,258)( 49,253)( 50,254)( 51,255)( 52,259)( 53,260)( 54,261)( 55,301)( 56,302)( 57,303)( 58,298)( 59,299)( 60,300)( 61,304)( 62,305)( 63,306)( 64,319)( 65,320)( 66,321)( 67,316)( 68,317)( 69,318)( 70,322)( 71,323)( 72,324)( 73,310)( 74,311)( 75,312)( 76,307)( 77,308)( 78,309)( 79,313)( 80,314)( 81,315)( 82,274)( 83,275)( 84,276)( 85,271)( 86,272)( 87,273)( 88,277)( 89,278)( 90,279)( 91,292)( 92,293)( 93,294)( 94,289)( 95,290)( 96,291)( 97,295)( 98,296)( 99,297)(100,283)(101,284)(102,285)(103,280)(104,281)(105,282)(106,286)(107,287)(108,288)(109,382)(110,383)(111,384)(112,379)(113,380)(114,381)(115,385)(116,386)(117,387)(118,400)(119,401)(120,402)(121,397)(122,398)(123,399)(124,403)(125,404)(126,405)(127,391)(128,392)(129,393)(130,388)(131,389)(132,390)(133,394)(134,395)(135,396)(136,409)(137,410)(138,411)(139,406)(140,407)(141,408)(142,412)(143,413)(144,414)(145,427)(146,428)(147,429)(148,424)(149,425)(150,426)(151,430)(152,431)(153,432)(154,418)(155,419)(156,420)(157,415)(158,416)(159,417)(160,421)(161,422)(162,423)(163,328)(164,329)(165,330)(166,325)(167,326)(168,327)(169,331)(170,332)(171,333)(172,346)(173,347)(174,348)(175,343)(176,344)(177,345)(178,349)(179,350)(180,351)(181,337)(182,338)(183,339)(184,334)(185,335)(186,336)(187,340)(188,341)(189,342)(190,355)(191,356)(192,357)(193,352)(194,353)(195,354)(196,358)(197,359)(198,360)(199,373)(200,374)(201,375)(202,370)(203,371)(204,372)(205,376)(206,377)(207,378)(208,364)(209,365)(210,366)(211,361)(212,362)(213,363)(214,367)(215,368)(216,369);
s2 := Sym(432)!(  1, 10)(  2, 12)(  3, 11)(  4, 14)(  5, 13)(  6, 15)(  7, 18)(  8, 17)(  9, 16)( 20, 21)( 22, 23)( 25, 27)( 28, 37)( 29, 39)( 30, 38)( 31, 41)( 32, 40)( 33, 42)( 34, 45)( 35, 44)( 36, 43)( 47, 48)( 49, 50)( 52, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 68)( 59, 67)( 60, 69)( 61, 72)( 62, 71)( 63, 70)( 74, 75)( 76, 77)( 79, 81)( 82, 91)( 83, 93)( 84, 92)( 85, 95)( 86, 94)( 87, 96)( 88, 99)( 89, 98)( 90, 97)(101,102)(103,104)(106,108)(109,118)(110,120)(111,119)(112,122)(113,121)(114,123)(115,126)(116,125)(117,124)(128,129)(130,131)(133,135)(136,145)(137,147)(138,146)(139,149)(140,148)(141,150)(142,153)(143,152)(144,151)(155,156)(157,158)(160,162)(163,172)(164,174)(165,173)(166,176)(167,175)(168,177)(169,180)(170,179)(171,178)(182,183)(184,185)(187,189)(190,199)(191,201)(192,200)(193,203)(194,202)(195,204)(196,207)(197,206)(198,205)(209,210)(211,212)(214,216)(217,226)(218,228)(219,227)(220,230)(221,229)(222,231)(223,234)(224,233)(225,232)(236,237)(238,239)(241,243)(244,253)(245,255)(246,254)(247,257)(248,256)(249,258)(250,261)(251,260)(252,259)(263,264)(265,266)(268,270)(271,280)(272,282)(273,281)(274,284)(275,283)(276,285)(277,288)(278,287)(279,286)(290,291)(292,293)(295,297)(298,307)(299,309)(300,308)(301,311)(302,310)(303,312)(304,315)(305,314)(306,313)(317,318)(319,320)(322,324)(325,334)(326,336)(327,335)(328,338)(329,337)(330,339)(331,342)(332,341)(333,340)(344,345)(346,347)(349,351)(352,361)(353,363)(354,362)(355,365)(356,364)(357,366)(358,369)(359,368)(360,367)(371,372)(373,374)(376,378)(379,388)(380,390)(381,389)(382,392)(383,391)(384,393)(385,396)(386,395)(387,394)(398,399)(400,401)(403,405)(406,415)(407,417)(408,416)(409,419)(410,418)(411,420)(412,423)(413,422)(414,421)(425,426)(427,428)(430,432);
poly := sub<Sym(432)|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*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*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 >;
References : None.
to this polytope

Twisty Puzzle