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Polytope of Type {48,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,18}*1728b
if this polytope has a name.
Group : SmallGroup(1728,5288)
Rank : 3
Schlafli Type : {48,18}
Number of vertices, edges, etc : 48, 432, 18
Order of s0s1s2 : 144
Order of s0s1s2s1 : 6
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 : {24,18}*864b
   3-fold quotients : {16,18}*576, {48,6}*576c
   4-fold quotients : {12,18}*432b
   6-fold quotients : {8,18}*288, {24,6}*288c
   8-fold quotients : {6,18}*216b
   9-fold quotients : {16,6}*192
   12-fold quotients : {4,18}*144a, {12,6}*144c
   16-fold quotients : {6,9}*108
   18-fold quotients : {8,6}*96
   24-fold quotients : {2,18}*72, {6,6}*72b
   27-fold quotients : {16,2}*64
   36-fold quotients : {4,6}*48a
   48-fold quotients : {2,9}*36, {6,3}*36
   54-fold quotients : {8,2}*32
   72-fold quotients : {2,6}*24
   108-fold quotients : {4,2}*16
   144-fold quotients : {2,3}*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)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)
( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)
( 50, 53)( 51, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)( 60, 90)
( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)( 68, 98)
( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)( 76,106)
( 77,107)( 78,108)( 79,103)( 80,104)( 81,105)(109,163)(110,164)(111,165)
(112,169)(113,170)(114,171)(115,166)(116,167)(117,168)(118,172)(119,173)
(120,174)(121,178)(122,179)(123,180)(124,175)(125,176)(126,177)(127,181)
(128,182)(129,183)(130,187)(131,188)(132,189)(133,184)(134,185)(135,186)
(136,190)(137,191)(138,192)(139,196)(140,197)(141,198)(142,193)(143,194)
(144,195)(145,199)(146,200)(147,201)(148,205)(149,206)(150,207)(151,202)
(152,203)(153,204)(154,208)(155,209)(156,210)(157,214)(158,215)(159,216)
(160,211)(161,212)(162,213)(217,325)(218,326)(219,327)(220,331)(221,332)
(222,333)(223,328)(224,329)(225,330)(226,334)(227,335)(228,336)(229,340)
(230,341)(231,342)(232,337)(233,338)(234,339)(235,343)(236,344)(237,345)
(238,349)(239,350)(240,351)(241,346)(242,347)(243,348)(244,352)(245,353)
(246,354)(247,358)(248,359)(249,360)(250,355)(251,356)(252,357)(253,361)
(254,362)(255,363)(256,367)(257,368)(258,369)(259,364)(260,365)(261,366)
(262,370)(263,371)(264,372)(265,376)(266,377)(267,378)(268,373)(269,374)
(270,375)(271,406)(272,407)(273,408)(274,412)(275,413)(276,414)(277,409)
(278,410)(279,411)(280,415)(281,416)(282,417)(283,421)(284,422)(285,423)
(286,418)(287,419)(288,420)(289,424)(290,425)(291,426)(292,430)(293,431)
(294,432)(295,427)(296,428)(297,429)(298,379)(299,380)(300,381)(301,385)
(302,386)(303,387)(304,382)(305,383)(306,384)(307,388)(308,389)(309,390)
(310,394)(311,395)(312,396)(313,391)(314,392)(315,393)(316,397)(317,398)
(318,399)(319,403)(320,404)(321,405)(322,400)(323,401)(324,402);;
s1 := (  1,220)(  2,222)(  3,221)(  4,217)(  5,219)(  6,218)(  7,223)(  8,225)
(  9,224)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)( 16,243)
( 17,242)( 18,241)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)( 24,226)
( 25,234)( 26,233)( 27,232)( 28,247)( 29,249)( 30,248)( 31,244)( 32,246)
( 33,245)( 34,250)( 35,252)( 36,251)( 37,267)( 38,266)( 39,265)( 40,264)
( 41,263)( 42,262)( 43,270)( 44,269)( 45,268)( 46,258)( 47,257)( 48,256)
( 49,255)( 50,254)( 51,253)( 52,261)( 53,260)( 54,259)( 55,301)( 56,303)
( 57,302)( 58,298)( 59,300)( 60,299)( 61,304)( 62,306)( 63,305)( 64,321)
( 65,320)( 66,319)( 67,318)( 68,317)( 69,316)( 70,324)( 71,323)( 72,322)
( 73,312)( 74,311)( 75,310)( 76,309)( 77,308)( 78,307)( 79,315)( 80,314)
( 81,313)( 82,274)( 83,276)( 84,275)( 85,271)( 86,273)( 87,272)( 88,277)
( 89,279)( 90,278)( 91,294)( 92,293)( 93,292)( 94,291)( 95,290)( 96,289)
( 97,297)( 98,296)( 99,295)(100,285)(101,284)(102,283)(103,282)(104,281)
(105,280)(106,288)(107,287)(108,286)(109,382)(110,384)(111,383)(112,379)
(113,381)(114,380)(115,385)(116,387)(117,386)(118,402)(119,401)(120,400)
(121,399)(122,398)(123,397)(124,405)(125,404)(126,403)(127,393)(128,392)
(129,391)(130,390)(131,389)(132,388)(133,396)(134,395)(135,394)(136,409)
(137,411)(138,410)(139,406)(140,408)(141,407)(142,412)(143,414)(144,413)
(145,429)(146,428)(147,427)(148,426)(149,425)(150,424)(151,432)(152,431)
(153,430)(154,420)(155,419)(156,418)(157,417)(158,416)(159,415)(160,423)
(161,422)(162,421)(163,328)(164,330)(165,329)(166,325)(167,327)(168,326)
(169,331)(170,333)(171,332)(172,348)(173,347)(174,346)(175,345)(176,344)
(177,343)(178,351)(179,350)(180,349)(181,339)(182,338)(183,337)(184,336)
(185,335)(186,334)(187,342)(188,341)(189,340)(190,355)(191,357)(192,356)
(193,352)(194,354)(195,353)(196,358)(197,360)(198,359)(199,375)(200,374)
(201,373)(202,372)(203,371)(204,370)(205,378)(206,377)(207,376)(208,366)
(209,365)(210,364)(211,363)(212,362)(213,361)(214,369)(215,368)(216,367);;
s2 := (  1, 10)(  2, 12)(  3, 11)(  4, 16)(  5, 18)(  6, 17)(  7, 13)(  8, 15)
(  9, 14)( 19, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 37)( 29, 39)( 30, 38)
( 31, 43)( 32, 45)( 33, 44)( 34, 40)( 35, 42)( 36, 41)( 46, 48)( 49, 54)
( 50, 53)( 51, 52)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)( 60, 71)
( 61, 67)( 62, 69)( 63, 68)( 73, 75)( 76, 81)( 77, 80)( 78, 79)( 82, 91)
( 83, 93)( 84, 92)( 85, 97)( 86, 99)( 87, 98)( 88, 94)( 89, 96)( 90, 95)
(100,102)(103,108)(104,107)(105,106)(109,118)(110,120)(111,119)(112,124)
(113,126)(114,125)(115,121)(116,123)(117,122)(127,129)(130,135)(131,134)
(132,133)(136,145)(137,147)(138,146)(139,151)(140,153)(141,152)(142,148)
(143,150)(144,149)(154,156)(157,162)(158,161)(159,160)(163,172)(164,174)
(165,173)(166,178)(167,180)(168,179)(169,175)(170,177)(171,176)(181,183)
(184,189)(185,188)(186,187)(190,199)(191,201)(192,200)(193,205)(194,207)
(195,206)(196,202)(197,204)(198,203)(208,210)(211,216)(212,215)(213,214)
(217,226)(218,228)(219,227)(220,232)(221,234)(222,233)(223,229)(224,231)
(225,230)(235,237)(238,243)(239,242)(240,241)(244,253)(245,255)(246,254)
(247,259)(248,261)(249,260)(250,256)(251,258)(252,257)(262,264)(265,270)
(266,269)(267,268)(271,280)(272,282)(273,281)(274,286)(275,288)(276,287)
(277,283)(278,285)(279,284)(289,291)(292,297)(293,296)(294,295)(298,307)
(299,309)(300,308)(301,313)(302,315)(303,314)(304,310)(305,312)(306,311)
(316,318)(319,324)(320,323)(321,322)(325,334)(326,336)(327,335)(328,340)
(329,342)(330,341)(331,337)(332,339)(333,338)(343,345)(346,351)(347,350)
(348,349)(352,361)(353,363)(354,362)(355,367)(356,369)(357,368)(358,364)
(359,366)(360,365)(370,372)(373,378)(374,377)(375,376)(379,388)(380,390)
(381,389)(382,394)(383,396)(384,395)(385,391)(386,393)(387,392)(397,399)
(400,405)(401,404)(402,403)(406,415)(407,417)(408,416)(409,421)(410,423)
(411,422)(412,418)(413,420)(414,419)(424,426)(427,432)(428,431)(429,430);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s0*s1*s0*s2*s1*s0*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(432)!(  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)
( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)
( 49, 52)( 50, 53)( 51, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)
( 60, 90)( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)
( 68, 98)( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)
( 76,106)( 77,107)( 78,108)( 79,103)( 80,104)( 81,105)(109,163)(110,164)
(111,165)(112,169)(113,170)(114,171)(115,166)(116,167)(117,168)(118,172)
(119,173)(120,174)(121,178)(122,179)(123,180)(124,175)(125,176)(126,177)
(127,181)(128,182)(129,183)(130,187)(131,188)(132,189)(133,184)(134,185)
(135,186)(136,190)(137,191)(138,192)(139,196)(140,197)(141,198)(142,193)
(143,194)(144,195)(145,199)(146,200)(147,201)(148,205)(149,206)(150,207)
(151,202)(152,203)(153,204)(154,208)(155,209)(156,210)(157,214)(158,215)
(159,216)(160,211)(161,212)(162,213)(217,325)(218,326)(219,327)(220,331)
(221,332)(222,333)(223,328)(224,329)(225,330)(226,334)(227,335)(228,336)
(229,340)(230,341)(231,342)(232,337)(233,338)(234,339)(235,343)(236,344)
(237,345)(238,349)(239,350)(240,351)(241,346)(242,347)(243,348)(244,352)
(245,353)(246,354)(247,358)(248,359)(249,360)(250,355)(251,356)(252,357)
(253,361)(254,362)(255,363)(256,367)(257,368)(258,369)(259,364)(260,365)
(261,366)(262,370)(263,371)(264,372)(265,376)(266,377)(267,378)(268,373)
(269,374)(270,375)(271,406)(272,407)(273,408)(274,412)(275,413)(276,414)
(277,409)(278,410)(279,411)(280,415)(281,416)(282,417)(283,421)(284,422)
(285,423)(286,418)(287,419)(288,420)(289,424)(290,425)(291,426)(292,430)
(293,431)(294,432)(295,427)(296,428)(297,429)(298,379)(299,380)(300,381)
(301,385)(302,386)(303,387)(304,382)(305,383)(306,384)(307,388)(308,389)
(309,390)(310,394)(311,395)(312,396)(313,391)(314,392)(315,393)(316,397)
(317,398)(318,399)(319,403)(320,404)(321,405)(322,400)(323,401)(324,402);
s1 := Sym(432)!(  1,220)(  2,222)(  3,221)(  4,217)(  5,219)(  6,218)(  7,223)
(  8,225)(  9,224)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)
( 16,243)( 17,242)( 18,241)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)
( 24,226)( 25,234)( 26,233)( 27,232)( 28,247)( 29,249)( 30,248)( 31,244)
( 32,246)( 33,245)( 34,250)( 35,252)( 36,251)( 37,267)( 38,266)( 39,265)
( 40,264)( 41,263)( 42,262)( 43,270)( 44,269)( 45,268)( 46,258)( 47,257)
( 48,256)( 49,255)( 50,254)( 51,253)( 52,261)( 53,260)( 54,259)( 55,301)
( 56,303)( 57,302)( 58,298)( 59,300)( 60,299)( 61,304)( 62,306)( 63,305)
( 64,321)( 65,320)( 66,319)( 67,318)( 68,317)( 69,316)( 70,324)( 71,323)
( 72,322)( 73,312)( 74,311)( 75,310)( 76,309)( 77,308)( 78,307)( 79,315)
( 80,314)( 81,313)( 82,274)( 83,276)( 84,275)( 85,271)( 86,273)( 87,272)
( 88,277)( 89,279)( 90,278)( 91,294)( 92,293)( 93,292)( 94,291)( 95,290)
( 96,289)( 97,297)( 98,296)( 99,295)(100,285)(101,284)(102,283)(103,282)
(104,281)(105,280)(106,288)(107,287)(108,286)(109,382)(110,384)(111,383)
(112,379)(113,381)(114,380)(115,385)(116,387)(117,386)(118,402)(119,401)
(120,400)(121,399)(122,398)(123,397)(124,405)(125,404)(126,403)(127,393)
(128,392)(129,391)(130,390)(131,389)(132,388)(133,396)(134,395)(135,394)
(136,409)(137,411)(138,410)(139,406)(140,408)(141,407)(142,412)(143,414)
(144,413)(145,429)(146,428)(147,427)(148,426)(149,425)(150,424)(151,432)
(152,431)(153,430)(154,420)(155,419)(156,418)(157,417)(158,416)(159,415)
(160,423)(161,422)(162,421)(163,328)(164,330)(165,329)(166,325)(167,327)
(168,326)(169,331)(170,333)(171,332)(172,348)(173,347)(174,346)(175,345)
(176,344)(177,343)(178,351)(179,350)(180,349)(181,339)(182,338)(183,337)
(184,336)(185,335)(186,334)(187,342)(188,341)(189,340)(190,355)(191,357)
(192,356)(193,352)(194,354)(195,353)(196,358)(197,360)(198,359)(199,375)
(200,374)(201,373)(202,372)(203,371)(204,370)(205,378)(206,377)(207,376)
(208,366)(209,365)(210,364)(211,363)(212,362)(213,361)(214,369)(215,368)
(216,367);
s2 := Sym(432)!(  1, 10)(  2, 12)(  3, 11)(  4, 16)(  5, 18)(  6, 17)(  7, 13)
(  8, 15)(  9, 14)( 19, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 37)( 29, 39)
( 30, 38)( 31, 43)( 32, 45)( 33, 44)( 34, 40)( 35, 42)( 36, 41)( 46, 48)
( 49, 54)( 50, 53)( 51, 52)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)
( 60, 71)( 61, 67)( 62, 69)( 63, 68)( 73, 75)( 76, 81)( 77, 80)( 78, 79)
( 82, 91)( 83, 93)( 84, 92)( 85, 97)( 86, 99)( 87, 98)( 88, 94)( 89, 96)
( 90, 95)(100,102)(103,108)(104,107)(105,106)(109,118)(110,120)(111,119)
(112,124)(113,126)(114,125)(115,121)(116,123)(117,122)(127,129)(130,135)
(131,134)(132,133)(136,145)(137,147)(138,146)(139,151)(140,153)(141,152)
(142,148)(143,150)(144,149)(154,156)(157,162)(158,161)(159,160)(163,172)
(164,174)(165,173)(166,178)(167,180)(168,179)(169,175)(170,177)(171,176)
(181,183)(184,189)(185,188)(186,187)(190,199)(191,201)(192,200)(193,205)
(194,207)(195,206)(196,202)(197,204)(198,203)(208,210)(211,216)(212,215)
(213,214)(217,226)(218,228)(219,227)(220,232)(221,234)(222,233)(223,229)
(224,231)(225,230)(235,237)(238,243)(239,242)(240,241)(244,253)(245,255)
(246,254)(247,259)(248,261)(249,260)(250,256)(251,258)(252,257)(262,264)
(265,270)(266,269)(267,268)(271,280)(272,282)(273,281)(274,286)(275,288)
(276,287)(277,283)(278,285)(279,284)(289,291)(292,297)(293,296)(294,295)
(298,307)(299,309)(300,308)(301,313)(302,315)(303,314)(304,310)(305,312)
(306,311)(316,318)(319,324)(320,323)(321,322)(325,334)(326,336)(327,335)
(328,340)(329,342)(330,341)(331,337)(332,339)(333,338)(343,345)(346,351)
(347,350)(348,349)(352,361)(353,363)(354,362)(355,367)(356,369)(357,368)
(358,364)(359,366)(360,365)(370,372)(373,378)(374,377)(375,376)(379,388)
(380,390)(381,389)(382,394)(383,396)(384,395)(385,391)(386,393)(387,392)
(397,399)(400,405)(401,404)(402,403)(406,415)(407,417)(408,416)(409,421)
(410,423)(411,422)(412,418)(413,420)(414,419)(424,426)(427,432)(428,431)
(429,430);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s0*s1*s0*s2*s1*s0*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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