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Polytope of Type {48,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6}*1728a
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}*864a
   3-fold quotients : {48,6}*576b
   4-fold quotients : {12,6}*432a
   6-fold quotients : {24,6}*288b
   8-fold quotients : {6,6}*216c
   9-fold quotients : {48,2}*192
   12-fold quotients : {12,6}*144b
   16-fold quotients : {3,6}*108
   18-fold quotients : {24,2}*96
   24-fold quotients : {6,6}*72c
   27-fold quotients : {16,2}*64
   36-fold quotients : {12,2}*48
   48-fold quotients : {3,6}*36
   54-fold quotients : {8,2}*32
   72-fold quotients : {6,2}*24
   108-fold quotients : {4,2}*16
   144-fold quotients : {3,2}*12
   216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  4,  7)(  5,  8)(  6,  9)( 10, 19)( 11, 20)( 12, 21)( 13, 25)( 14, 26)
( 15, 27)( 16, 22)( 17, 23)( 18, 24)( 31, 34)( 32, 35)( 33, 36)( 37, 46)
( 38, 47)( 39, 48)( 40, 52)( 41, 53)( 42, 54)( 43, 49)( 44, 50)( 45, 51)
( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)( 60, 90)( 61, 85)( 62, 86)
( 63, 87)( 64,100)( 65,101)( 66,102)( 67,106)( 68,107)( 69,108)( 70,103)
( 71,104)( 72,105)( 73, 91)( 74, 92)( 75, 93)( 76, 97)( 77, 98)( 78, 99)
( 79, 94)( 80, 95)( 81, 96)(109,163)(110,164)(111,165)(112,169)(113,170)
(114,171)(115,166)(116,167)(117,168)(118,181)(119,182)(120,183)(121,187)
(122,188)(123,189)(124,184)(125,185)(126,186)(127,172)(128,173)(129,174)
(130,178)(131,179)(132,180)(133,175)(134,176)(135,177)(136,190)(137,191)
(138,192)(139,196)(140,197)(141,198)(142,193)(143,194)(144,195)(145,208)
(146,209)(147,210)(148,214)(149,215)(150,216)(151,211)(152,212)(153,213)
(154,199)(155,200)(156,201)(157,205)(158,206)(159,207)(160,202)(161,203)
(162,204)(217,325)(218,326)(219,327)(220,331)(221,332)(222,333)(223,328)
(224,329)(225,330)(226,343)(227,344)(228,345)(229,349)(230,350)(231,351)
(232,346)(233,347)(234,348)(235,334)(236,335)(237,336)(238,340)(239,341)
(240,342)(241,337)(242,338)(243,339)(244,352)(245,353)(246,354)(247,358)
(248,359)(249,360)(250,355)(251,356)(252,357)(253,370)(254,371)(255,372)
(256,376)(257,377)(258,378)(259,373)(260,374)(261,375)(262,361)(263,362)
(264,363)(265,367)(266,368)(267,369)(268,364)(269,365)(270,366)(271,406)
(272,407)(273,408)(274,412)(275,413)(276,414)(277,409)(278,410)(279,411)
(280,424)(281,425)(282,426)(283,430)(284,431)(285,432)(286,427)(287,428)
(288,429)(289,415)(290,416)(291,417)(292,421)(293,422)(294,423)(295,418)
(296,419)(297,420)(298,379)(299,380)(300,381)(301,385)(302,386)(303,387)
(304,382)(305,383)(306,384)(307,397)(308,398)(309,399)(310,403)(311,404)
(312,405)(313,400)(314,401)(315,402)(316,388)(317,389)(318,390)(319,394)
(320,395)(321,396)(322,391)(323,392)(324,393);;
s1 := (  1,239)(  2,240)(  3,238)(  4,237)(  5,235)(  6,236)(  7,241)(  8,242)
(  9,243)( 10,230)( 11,231)( 12,229)( 13,228)( 14,226)( 15,227)( 16,232)
( 17,233)( 18,234)( 19,221)( 20,222)( 21,220)( 22,219)( 23,217)( 24,218)
( 25,223)( 26,224)( 27,225)( 28,266)( 29,267)( 30,265)( 31,264)( 32,262)
( 33,263)( 34,268)( 35,269)( 36,270)( 37,257)( 38,258)( 39,256)( 40,255)
( 41,253)( 42,254)( 43,259)( 44,260)( 45,261)( 46,248)( 47,249)( 48,247)
( 49,246)( 50,244)( 51,245)( 52,250)( 53,251)( 54,252)( 55,320)( 56,321)
( 57,319)( 58,318)( 59,316)( 60,317)( 61,322)( 62,323)( 63,324)( 64,311)
( 65,312)( 66,310)( 67,309)( 68,307)( 69,308)( 70,313)( 71,314)( 72,315)
( 73,302)( 74,303)( 75,301)( 76,300)( 77,298)( 78,299)( 79,304)( 80,305)
( 81,306)( 82,293)( 83,294)( 84,292)( 85,291)( 86,289)( 87,290)( 88,295)
( 89,296)( 90,297)( 91,284)( 92,285)( 93,283)( 94,282)( 95,280)( 96,281)
( 97,286)( 98,287)( 99,288)(100,275)(101,276)(102,274)(103,273)(104,271)
(105,272)(106,277)(107,278)(108,279)(109,401)(110,402)(111,400)(112,399)
(113,397)(114,398)(115,403)(116,404)(117,405)(118,392)(119,393)(120,391)
(121,390)(122,388)(123,389)(124,394)(125,395)(126,396)(127,383)(128,384)
(129,382)(130,381)(131,379)(132,380)(133,385)(134,386)(135,387)(136,428)
(137,429)(138,427)(139,426)(140,424)(141,425)(142,430)(143,431)(144,432)
(145,419)(146,420)(147,418)(148,417)(149,415)(150,416)(151,421)(152,422)
(153,423)(154,410)(155,411)(156,409)(157,408)(158,406)(159,407)(160,412)
(161,413)(162,414)(163,347)(164,348)(165,346)(166,345)(167,343)(168,344)
(169,349)(170,350)(171,351)(172,338)(173,339)(174,337)(175,336)(176,334)
(177,335)(178,340)(179,341)(180,342)(181,329)(182,330)(183,328)(184,327)
(185,325)(186,326)(187,331)(188,332)(189,333)(190,374)(191,375)(192,373)
(193,372)(194,370)(195,371)(196,376)(197,377)(198,378)(199,365)(200,366)
(201,364)(202,363)(203,361)(204,362)(205,367)(206,368)(207,369)(208,356)
(209,357)(210,355)(211,354)(212,352)(213,353)(214,358)(215,359)(216,360);;
s2 := (  2,  3)(  5,  6)(  8,  9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)( 14, 24)
( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)( 37, 46)
( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)( 45, 53)
( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)( 68, 78)
( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 83, 84)( 86, 87)( 89, 90)( 91,100)
( 92,102)( 93,101)( 94,103)( 95,105)( 96,104)( 97,106)( 98,108)( 99,107)
(110,111)(113,114)(116,117)(118,127)(119,129)(120,128)(121,130)(122,132)
(123,131)(124,133)(125,135)(126,134)(137,138)(140,141)(143,144)(145,154)
(146,156)(147,155)(148,157)(149,159)(150,158)(151,160)(152,162)(153,161)
(164,165)(167,168)(170,171)(172,181)(173,183)(174,182)(175,184)(176,186)
(177,185)(178,187)(179,189)(180,188)(191,192)(194,195)(197,198)(199,208)
(200,210)(201,209)(202,211)(203,213)(204,212)(205,214)(206,216)(207,215)
(218,219)(221,222)(224,225)(226,235)(227,237)(228,236)(229,238)(230,240)
(231,239)(232,241)(233,243)(234,242)(245,246)(248,249)(251,252)(253,262)
(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)(261,269)
(272,273)(275,276)(278,279)(280,289)(281,291)(282,290)(283,292)(284,294)
(285,293)(286,295)(287,297)(288,296)(299,300)(302,303)(305,306)(307,316)
(308,318)(309,317)(310,319)(311,321)(312,320)(313,322)(314,324)(315,323)
(326,327)(329,330)(332,333)(334,343)(335,345)(336,344)(337,346)(338,348)
(339,347)(340,349)(341,351)(342,350)(353,354)(356,357)(359,360)(361,370)
(362,372)(363,371)(364,373)(365,375)(366,374)(367,376)(368,378)(369,377)
(380,381)(383,384)(386,387)(388,397)(389,399)(390,398)(391,400)(392,402)
(393,401)(394,403)(395,405)(396,404)(407,408)(410,411)(413,414)(415,424)
(416,426)(417,425)(418,427)(419,429)(420,428)(421,430)(422,432)(423,431);;
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*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(432)!(  4,  7)(  5,  8)(  6,  9)( 10, 19)( 11, 20)( 12, 21)( 13, 25)
( 14, 26)( 15, 27)( 16, 22)( 17, 23)( 18, 24)( 31, 34)( 32, 35)( 33, 36)
( 37, 46)( 38, 47)( 39, 48)( 40, 52)( 41, 53)( 42, 54)( 43, 49)( 44, 50)
( 45, 51)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)( 60, 90)( 61, 85)
( 62, 86)( 63, 87)( 64,100)( 65,101)( 66,102)( 67,106)( 68,107)( 69,108)
( 70,103)( 71,104)( 72,105)( 73, 91)( 74, 92)( 75, 93)( 76, 97)( 77, 98)
( 78, 99)( 79, 94)( 80, 95)( 81, 96)(109,163)(110,164)(111,165)(112,169)
(113,170)(114,171)(115,166)(116,167)(117,168)(118,181)(119,182)(120,183)
(121,187)(122,188)(123,189)(124,184)(125,185)(126,186)(127,172)(128,173)
(129,174)(130,178)(131,179)(132,180)(133,175)(134,176)(135,177)(136,190)
(137,191)(138,192)(139,196)(140,197)(141,198)(142,193)(143,194)(144,195)
(145,208)(146,209)(147,210)(148,214)(149,215)(150,216)(151,211)(152,212)
(153,213)(154,199)(155,200)(156,201)(157,205)(158,206)(159,207)(160,202)
(161,203)(162,204)(217,325)(218,326)(219,327)(220,331)(221,332)(222,333)
(223,328)(224,329)(225,330)(226,343)(227,344)(228,345)(229,349)(230,350)
(231,351)(232,346)(233,347)(234,348)(235,334)(236,335)(237,336)(238,340)
(239,341)(240,342)(241,337)(242,338)(243,339)(244,352)(245,353)(246,354)
(247,358)(248,359)(249,360)(250,355)(251,356)(252,357)(253,370)(254,371)
(255,372)(256,376)(257,377)(258,378)(259,373)(260,374)(261,375)(262,361)
(263,362)(264,363)(265,367)(266,368)(267,369)(268,364)(269,365)(270,366)
(271,406)(272,407)(273,408)(274,412)(275,413)(276,414)(277,409)(278,410)
(279,411)(280,424)(281,425)(282,426)(283,430)(284,431)(285,432)(286,427)
(287,428)(288,429)(289,415)(290,416)(291,417)(292,421)(293,422)(294,423)
(295,418)(296,419)(297,420)(298,379)(299,380)(300,381)(301,385)(302,386)
(303,387)(304,382)(305,383)(306,384)(307,397)(308,398)(309,399)(310,403)
(311,404)(312,405)(313,400)(314,401)(315,402)(316,388)(317,389)(318,390)
(319,394)(320,395)(321,396)(322,391)(323,392)(324,393);
s1 := Sym(432)!(  1,239)(  2,240)(  3,238)(  4,237)(  5,235)(  6,236)(  7,241)
(  8,242)(  9,243)( 10,230)( 11,231)( 12,229)( 13,228)( 14,226)( 15,227)
( 16,232)( 17,233)( 18,234)( 19,221)( 20,222)( 21,220)( 22,219)( 23,217)
( 24,218)( 25,223)( 26,224)( 27,225)( 28,266)( 29,267)( 30,265)( 31,264)
( 32,262)( 33,263)( 34,268)( 35,269)( 36,270)( 37,257)( 38,258)( 39,256)
( 40,255)( 41,253)( 42,254)( 43,259)( 44,260)( 45,261)( 46,248)( 47,249)
( 48,247)( 49,246)( 50,244)( 51,245)( 52,250)( 53,251)( 54,252)( 55,320)
( 56,321)( 57,319)( 58,318)( 59,316)( 60,317)( 61,322)( 62,323)( 63,324)
( 64,311)( 65,312)( 66,310)( 67,309)( 68,307)( 69,308)( 70,313)( 71,314)
( 72,315)( 73,302)( 74,303)( 75,301)( 76,300)( 77,298)( 78,299)( 79,304)
( 80,305)( 81,306)( 82,293)( 83,294)( 84,292)( 85,291)( 86,289)( 87,290)
( 88,295)( 89,296)( 90,297)( 91,284)( 92,285)( 93,283)( 94,282)( 95,280)
( 96,281)( 97,286)( 98,287)( 99,288)(100,275)(101,276)(102,274)(103,273)
(104,271)(105,272)(106,277)(107,278)(108,279)(109,401)(110,402)(111,400)
(112,399)(113,397)(114,398)(115,403)(116,404)(117,405)(118,392)(119,393)
(120,391)(121,390)(122,388)(123,389)(124,394)(125,395)(126,396)(127,383)
(128,384)(129,382)(130,381)(131,379)(132,380)(133,385)(134,386)(135,387)
(136,428)(137,429)(138,427)(139,426)(140,424)(141,425)(142,430)(143,431)
(144,432)(145,419)(146,420)(147,418)(148,417)(149,415)(150,416)(151,421)
(152,422)(153,423)(154,410)(155,411)(156,409)(157,408)(158,406)(159,407)
(160,412)(161,413)(162,414)(163,347)(164,348)(165,346)(166,345)(167,343)
(168,344)(169,349)(170,350)(171,351)(172,338)(173,339)(174,337)(175,336)
(176,334)(177,335)(178,340)(179,341)(180,342)(181,329)(182,330)(183,328)
(184,327)(185,325)(186,326)(187,331)(188,332)(189,333)(190,374)(191,375)
(192,373)(193,372)(194,370)(195,371)(196,376)(197,377)(198,378)(199,365)
(200,366)(201,364)(202,363)(203,361)(204,362)(205,367)(206,368)(207,369)
(208,356)(209,357)(210,355)(211,354)(212,352)(213,353)(214,358)(215,359)
(216,360);
s2 := Sym(432)!(  2,  3)(  5,  6)(  8,  9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)
( 14, 24)( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)
( 37, 46)( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)
( 45, 53)( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)
( 68, 78)( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 83, 84)( 86, 87)( 89, 90)
( 91,100)( 92,102)( 93,101)( 94,103)( 95,105)( 96,104)( 97,106)( 98,108)
( 99,107)(110,111)(113,114)(116,117)(118,127)(119,129)(120,128)(121,130)
(122,132)(123,131)(124,133)(125,135)(126,134)(137,138)(140,141)(143,144)
(145,154)(146,156)(147,155)(148,157)(149,159)(150,158)(151,160)(152,162)
(153,161)(164,165)(167,168)(170,171)(172,181)(173,183)(174,182)(175,184)
(176,186)(177,185)(178,187)(179,189)(180,188)(191,192)(194,195)(197,198)
(199,208)(200,210)(201,209)(202,211)(203,213)(204,212)(205,214)(206,216)
(207,215)(218,219)(221,222)(224,225)(226,235)(227,237)(228,236)(229,238)
(230,240)(231,239)(232,241)(233,243)(234,242)(245,246)(248,249)(251,252)
(253,262)(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)
(261,269)(272,273)(275,276)(278,279)(280,289)(281,291)(282,290)(283,292)
(284,294)(285,293)(286,295)(287,297)(288,296)(299,300)(302,303)(305,306)
(307,316)(308,318)(309,317)(310,319)(311,321)(312,320)(313,322)(314,324)
(315,323)(326,327)(329,330)(332,333)(334,343)(335,345)(336,344)(337,346)
(338,348)(339,347)(340,349)(341,351)(342,350)(353,354)(356,357)(359,360)
(361,370)(362,372)(363,371)(364,373)(365,375)(366,374)(367,376)(368,378)
(369,377)(380,381)(383,384)(386,387)(388,397)(389,399)(390,398)(391,400)
(392,402)(393,401)(394,403)(395,405)(396,404)(407,408)(410,411)(413,414)
(415,424)(416,426)(417,425)(418,427)(419,429)(420,428)(421,430)(422,432)
(423,431);
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, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*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 >; 
 
References : None.
to this polytope