Polytope of Type {18,48}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,48}*1728a
Also Known As : {18,48|2}. if this polytope has another name.
Group : SmallGroup(1728,3040)
Rank : 3
Schlafli Type : {18,48}
Number of vertices, edges, etc : 18, 432, 48
Order of s0s1s2 : 144
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 : {18,24}*864a
3-fold quotients : {18,16}*576, {6,48}*576a
4-fold quotients : {18,12}*432a
6-fold quotients : {18,8}*288, {6,24}*288a
8-fold quotients : {18,6}*216a
9-fold quotients : {2,48}*192, {6,16}*192
12-fold quotients : {18,4}*144a, {6,12}*144a
18-fold quotients : {2,24}*96, {6,8}*96
24-fold quotients : {18,2}*72, {6,6}*72a
27-fold quotients : {2,16}*64
36-fold quotients : {2,12}*48, {6,4}*48a
48-fold quotients : {9,2}*36
54-fold quotients : {2,8}*32
72-fold quotients : {2,6}*24, {6,2}*24
108-fold quotients : {2,4}*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.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)( 10, 21)( 11, 20)( 12, 19)( 13, 24)( 14, 23)
( 15, 22)( 16, 27)( 17, 26)( 18, 25)( 29, 30)( 32, 33)( 35, 36)( 37, 48)
( 38, 47)( 39, 46)( 40, 51)( 41, 50)( 42, 49)( 43, 54)( 44, 53)( 45, 52)
( 56, 57)( 59, 60)( 62, 63)( 64, 75)( 65, 74)( 66, 73)( 67, 78)( 68, 77)
( 69, 76)( 70, 81)( 71, 80)( 72, 79)( 83, 84)( 86, 87)( 89, 90)( 91,102)
( 92,101)( 93,100)( 94,105)( 95,104)( 96,103)( 97,108)( 98,107)( 99,106)
(110,111)(113,114)(116,117)(118,129)(119,128)(120,127)(121,132)(122,131)
(123,130)(124,135)(125,134)(126,133)(137,138)(140,141)(143,144)(145,156)
(146,155)(147,154)(148,159)(149,158)(150,157)(151,162)(152,161)(153,160)
(164,165)(167,168)(170,171)(172,183)(173,182)(174,181)(175,186)(176,185)
(177,184)(178,189)(179,188)(180,187)(191,192)(194,195)(197,198)(199,210)
(200,209)(201,208)(202,213)(203,212)(204,211)(205,216)(206,215)(207,214)
(218,219)(221,222)(224,225)(226,237)(227,236)(228,235)(229,240)(230,239)
(231,238)(232,243)(233,242)(234,241)(245,246)(248,249)(251,252)(253,264)
(254,263)(255,262)(256,267)(257,266)(258,265)(259,270)(260,269)(261,268)
(272,273)(275,276)(278,279)(280,291)(281,290)(282,289)(283,294)(284,293)
(285,292)(286,297)(287,296)(288,295)(299,300)(302,303)(305,306)(307,318)
(308,317)(309,316)(310,321)(311,320)(312,319)(313,324)(314,323)(315,322)
(326,327)(329,330)(332,333)(334,345)(335,344)(336,343)(337,348)(338,347)
(339,346)(340,351)(341,350)(342,349)(353,354)(356,357)(359,360)(361,372)
(362,371)(363,370)(364,375)(365,374)(366,373)(367,378)(368,377)(369,376)
(380,381)(383,384)(386,387)(388,399)(389,398)(390,397)(391,402)(392,401)
(393,400)(394,405)(395,404)(396,403)(407,408)(410,411)(413,414)(415,426)
(416,425)(417,424)(418,429)(419,428)(420,427)(421,432)(422,431)(423,430);;
s1 := ( 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, 91)( 56, 93)( 57, 92)( 58, 97)( 59, 99)( 60, 98)
( 61, 94)( 62, 96)( 63, 95)( 64, 82)( 65, 84)( 66, 83)( 67, 88)( 68, 90)
( 69, 89)( 70, 85)( 71, 87)( 72, 86)( 73,102)( 74,101)( 75,100)( 76,108)
( 77,107)( 78,106)( 79,105)( 80,104)( 81,103)(109,172)(110,174)(111,173)
(112,178)(113,180)(114,179)(115,175)(116,177)(117,176)(118,163)(119,165)
(120,164)(121,169)(122,171)(123,170)(124,166)(125,168)(126,167)(127,183)
(128,182)(129,181)(130,189)(131,188)(132,187)(133,186)(134,185)(135,184)
(136,199)(137,201)(138,200)(139,205)(140,207)(141,206)(142,202)(143,204)
(144,203)(145,190)(146,192)(147,191)(148,196)(149,198)(150,197)(151,193)
(152,195)(153,194)(154,210)(155,209)(156,208)(157,216)(158,215)(159,214)
(160,213)(161,212)(162,211)(217,334)(218,336)(219,335)(220,340)(221,342)
(222,341)(223,337)(224,339)(225,338)(226,325)(227,327)(228,326)(229,331)
(230,333)(231,332)(232,328)(233,330)(234,329)(235,345)(236,344)(237,343)
(238,351)(239,350)(240,349)(241,348)(242,347)(243,346)(244,361)(245,363)
(246,362)(247,367)(248,369)(249,368)(250,364)(251,366)(252,365)(253,352)
(254,354)(255,353)(256,358)(257,360)(258,359)(259,355)(260,357)(261,356)
(262,372)(263,371)(264,370)(265,378)(266,377)(267,376)(268,375)(269,374)
(270,373)(271,415)(272,417)(273,416)(274,421)(275,423)(276,422)(277,418)
(278,420)(279,419)(280,406)(281,408)(282,407)(283,412)(284,414)(285,413)
(286,409)(287,411)(288,410)(289,426)(290,425)(291,424)(292,432)(293,431)
(294,430)(295,429)(296,428)(297,427)(298,388)(299,390)(300,389)(301,394)
(302,396)(303,395)(304,391)(305,393)(306,392)(307,379)(308,381)(309,380)
(310,385)(311,387)(312,386)(313,382)(314,384)(315,383)(316,399)(317,398)
(318,397)(319,405)(320,404)(321,403)(322,402)(323,401)(324,400);;
s2 := ( 1,220)( 2,221)( 3,222)( 4,217)( 5,218)( 6,219)( 7,223)( 8,224)
( 9,225)( 10,229)( 11,230)( 12,231)( 13,226)( 14,227)( 15,228)( 16,232)
( 17,233)( 18,234)( 19,238)( 20,239)( 21,240)( 22,235)( 23,236)( 24,237)
( 25,241)( 26,242)( 27,243)( 28,247)( 29,248)( 30,249)( 31,244)( 32,245)
( 33,246)( 34,250)( 35,251)( 36,252)( 37,256)( 38,257)( 39,258)( 40,253)
( 41,254)( 42,255)( 43,259)( 44,260)( 45,261)( 46,265)( 47,266)( 48,267)
( 49,262)( 50,263)( 51,264)( 52,268)( 53,269)( 54,270)( 55,301)( 56,302)
( 57,303)( 58,298)( 59,299)( 60,300)( 61,304)( 62,305)( 63,306)( 64,310)
( 65,311)( 66,312)( 67,307)( 68,308)( 69,309)( 70,313)( 71,314)( 72,315)
( 73,319)( 74,320)( 75,321)( 76,316)( 77,317)( 78,318)( 79,322)( 80,323)
( 81,324)( 82,274)( 83,275)( 84,276)( 85,271)( 86,272)( 87,273)( 88,277)
( 89,278)( 90,279)( 91,283)( 92,284)( 93,285)( 94,280)( 95,281)( 96,282)
( 97,286)( 98,287)( 99,288)(100,292)(101,293)(102,294)(103,289)(104,290)
(105,291)(106,295)(107,296)(108,297)(109,382)(110,383)(111,384)(112,379)
(113,380)(114,381)(115,385)(116,386)(117,387)(118,391)(119,392)(120,393)
(121,388)(122,389)(123,390)(124,394)(125,395)(126,396)(127,400)(128,401)
(129,402)(130,397)(131,398)(132,399)(133,403)(134,404)(135,405)(136,409)
(137,410)(138,411)(139,406)(140,407)(141,408)(142,412)(143,413)(144,414)
(145,418)(146,419)(147,420)(148,415)(149,416)(150,417)(151,421)(152,422)
(153,423)(154,427)(155,428)(156,429)(157,424)(158,425)(159,426)(160,430)
(161,431)(162,432)(163,328)(164,329)(165,330)(166,325)(167,326)(168,327)
(169,331)(170,332)(171,333)(172,337)(173,338)(174,339)(175,334)(176,335)
(177,336)(178,340)(179,341)(180,342)(181,346)(182,347)(183,348)(184,343)
(185,344)(186,345)(187,349)(188,350)(189,351)(190,355)(191,356)(192,357)
(193,352)(194,353)(195,354)(196,358)(197,359)(198,360)(199,364)(200,365)
(201,366)(202,361)(203,362)(204,363)(205,367)(206,368)(207,369)(208,373)
(209,374)(210,375)(211,370)(212,371)(213,372)(214,376)(215,377)(216,378);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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*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*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)!( 2, 3)( 5, 6)( 8, 9)( 10, 21)( 11, 20)( 12, 19)( 13, 24)
( 14, 23)( 15, 22)( 16, 27)( 17, 26)( 18, 25)( 29, 30)( 32, 33)( 35, 36)
( 37, 48)( 38, 47)( 39, 46)( 40, 51)( 41, 50)( 42, 49)( 43, 54)( 44, 53)
( 45, 52)( 56, 57)( 59, 60)( 62, 63)( 64, 75)( 65, 74)( 66, 73)( 67, 78)
( 68, 77)( 69, 76)( 70, 81)( 71, 80)( 72, 79)( 83, 84)( 86, 87)( 89, 90)
( 91,102)( 92,101)( 93,100)( 94,105)( 95,104)( 96,103)( 97,108)( 98,107)
( 99,106)(110,111)(113,114)(116,117)(118,129)(119,128)(120,127)(121,132)
(122,131)(123,130)(124,135)(125,134)(126,133)(137,138)(140,141)(143,144)
(145,156)(146,155)(147,154)(148,159)(149,158)(150,157)(151,162)(152,161)
(153,160)(164,165)(167,168)(170,171)(172,183)(173,182)(174,181)(175,186)
(176,185)(177,184)(178,189)(179,188)(180,187)(191,192)(194,195)(197,198)
(199,210)(200,209)(201,208)(202,213)(203,212)(204,211)(205,216)(206,215)
(207,214)(218,219)(221,222)(224,225)(226,237)(227,236)(228,235)(229,240)
(230,239)(231,238)(232,243)(233,242)(234,241)(245,246)(248,249)(251,252)
(253,264)(254,263)(255,262)(256,267)(257,266)(258,265)(259,270)(260,269)
(261,268)(272,273)(275,276)(278,279)(280,291)(281,290)(282,289)(283,294)
(284,293)(285,292)(286,297)(287,296)(288,295)(299,300)(302,303)(305,306)
(307,318)(308,317)(309,316)(310,321)(311,320)(312,319)(313,324)(314,323)
(315,322)(326,327)(329,330)(332,333)(334,345)(335,344)(336,343)(337,348)
(338,347)(339,346)(340,351)(341,350)(342,349)(353,354)(356,357)(359,360)
(361,372)(362,371)(363,370)(364,375)(365,374)(366,373)(367,378)(368,377)
(369,376)(380,381)(383,384)(386,387)(388,399)(389,398)(390,397)(391,402)
(392,401)(393,400)(394,405)(395,404)(396,403)(407,408)(410,411)(413,414)
(415,426)(416,425)(417,424)(418,429)(419,428)(420,427)(421,432)(422,431)
(423,430);
s1 := 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, 91)( 56, 93)( 57, 92)( 58, 97)( 59, 99)
( 60, 98)( 61, 94)( 62, 96)( 63, 95)( 64, 82)( 65, 84)( 66, 83)( 67, 88)
( 68, 90)( 69, 89)( 70, 85)( 71, 87)( 72, 86)( 73,102)( 74,101)( 75,100)
( 76,108)( 77,107)( 78,106)( 79,105)( 80,104)( 81,103)(109,172)(110,174)
(111,173)(112,178)(113,180)(114,179)(115,175)(116,177)(117,176)(118,163)
(119,165)(120,164)(121,169)(122,171)(123,170)(124,166)(125,168)(126,167)
(127,183)(128,182)(129,181)(130,189)(131,188)(132,187)(133,186)(134,185)
(135,184)(136,199)(137,201)(138,200)(139,205)(140,207)(141,206)(142,202)
(143,204)(144,203)(145,190)(146,192)(147,191)(148,196)(149,198)(150,197)
(151,193)(152,195)(153,194)(154,210)(155,209)(156,208)(157,216)(158,215)
(159,214)(160,213)(161,212)(162,211)(217,334)(218,336)(219,335)(220,340)
(221,342)(222,341)(223,337)(224,339)(225,338)(226,325)(227,327)(228,326)
(229,331)(230,333)(231,332)(232,328)(233,330)(234,329)(235,345)(236,344)
(237,343)(238,351)(239,350)(240,349)(241,348)(242,347)(243,346)(244,361)
(245,363)(246,362)(247,367)(248,369)(249,368)(250,364)(251,366)(252,365)
(253,352)(254,354)(255,353)(256,358)(257,360)(258,359)(259,355)(260,357)
(261,356)(262,372)(263,371)(264,370)(265,378)(266,377)(267,376)(268,375)
(269,374)(270,373)(271,415)(272,417)(273,416)(274,421)(275,423)(276,422)
(277,418)(278,420)(279,419)(280,406)(281,408)(282,407)(283,412)(284,414)
(285,413)(286,409)(287,411)(288,410)(289,426)(290,425)(291,424)(292,432)
(293,431)(294,430)(295,429)(296,428)(297,427)(298,388)(299,390)(300,389)
(301,394)(302,396)(303,395)(304,391)(305,393)(306,392)(307,379)(308,381)
(309,380)(310,385)(311,387)(312,386)(313,382)(314,384)(315,383)(316,399)
(317,398)(318,397)(319,405)(320,404)(321,403)(322,402)(323,401)(324,400);
s2 := Sym(432)!( 1,220)( 2,221)( 3,222)( 4,217)( 5,218)( 6,219)( 7,223)
( 8,224)( 9,225)( 10,229)( 11,230)( 12,231)( 13,226)( 14,227)( 15,228)
( 16,232)( 17,233)( 18,234)( 19,238)( 20,239)( 21,240)( 22,235)( 23,236)
( 24,237)( 25,241)( 26,242)( 27,243)( 28,247)( 29,248)( 30,249)( 31,244)
( 32,245)( 33,246)( 34,250)( 35,251)( 36,252)( 37,256)( 38,257)( 39,258)
( 40,253)( 41,254)( 42,255)( 43,259)( 44,260)( 45,261)( 46,265)( 47,266)
( 48,267)( 49,262)( 50,263)( 51,264)( 52,268)( 53,269)( 54,270)( 55,301)
( 56,302)( 57,303)( 58,298)( 59,299)( 60,300)( 61,304)( 62,305)( 63,306)
( 64,310)( 65,311)( 66,312)( 67,307)( 68,308)( 69,309)( 70,313)( 71,314)
( 72,315)( 73,319)( 74,320)( 75,321)( 76,316)( 77,317)( 78,318)( 79,322)
( 80,323)( 81,324)( 82,274)( 83,275)( 84,276)( 85,271)( 86,272)( 87,273)
( 88,277)( 89,278)( 90,279)( 91,283)( 92,284)( 93,285)( 94,280)( 95,281)
( 96,282)( 97,286)( 98,287)( 99,288)(100,292)(101,293)(102,294)(103,289)
(104,290)(105,291)(106,295)(107,296)(108,297)(109,382)(110,383)(111,384)
(112,379)(113,380)(114,381)(115,385)(116,386)(117,387)(118,391)(119,392)
(120,393)(121,388)(122,389)(123,390)(124,394)(125,395)(126,396)(127,400)
(128,401)(129,402)(130,397)(131,398)(132,399)(133,403)(134,404)(135,405)
(136,409)(137,410)(138,411)(139,406)(140,407)(141,408)(142,412)(143,413)
(144,414)(145,418)(146,419)(147,420)(148,415)(149,416)(150,417)(151,421)
(152,422)(153,423)(154,427)(155,428)(156,429)(157,424)(158,425)(159,426)
(160,430)(161,431)(162,432)(163,328)(164,329)(165,330)(166,325)(167,326)
(168,327)(169,331)(170,332)(171,333)(172,337)(173,338)(174,339)(175,334)
(176,335)(177,336)(178,340)(179,341)(180,342)(181,346)(182,347)(183,348)
(184,343)(185,344)(186,345)(187,349)(188,350)(189,351)(190,355)(191,356)
(192,357)(193,352)(194,353)(195,354)(196,358)(197,359)(198,360)(199,364)
(200,365)(201,366)(202,361)(203,362)(204,363)(205,367)(206,368)(207,369)
(208,373)(209,374)(210,375)(211,370)(212,371)(213,372)(214,376)(215,377)
(216,378);
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*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,
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*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*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