Polytope of Type {24,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,18}*1728e
if this polytope has a name.
Group : SmallGroup(1728,30284)
Rank : 3
Schlafli Type : {24,18}
Number of vertices, edges, etc : 48, 432, 36
Order of s0s1s2 : 36
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {12,18}*864a
3-fold quotients : {8,18}*576b, {24,6}*576e
4-fold quotients : {12,18}*432c
6-fold quotients : {8,9}*288, {4,18}*288, {12,6}*288a
8-fold quotients : {6,18}*216a
9-fold quotients : {8,6}*192b
12-fold quotients : {4,9}*144, {4,18}*144b, {4,18}*144c, {12,6}*144d
18-fold quotients : {8,3}*96, {4,6}*96
24-fold quotients : {4,9}*72, {2,18}*72, {6,6}*72a
36-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
48-fold quotients : {2,9}*36
72-fold quotients : {4,3}*24, {2,6}*24, {6,2}*24
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 := ( 1,221)( 2,222)( 3,224)( 4,223)( 5,218)( 6,217)( 7,219)( 8,220)
( 9,229)( 10,230)( 11,232)( 12,231)( 13,226)( 14,225)( 15,227)( 16,228)
( 17,237)( 18,238)( 19,240)( 20,239)( 21,234)( 22,233)( 23,235)( 24,236)
( 25,269)( 26,270)( 27,272)( 28,271)( 29,266)( 30,265)( 31,267)( 32,268)
( 33,277)( 34,278)( 35,280)( 36,279)( 37,274)( 38,273)( 39,275)( 40,276)
( 41,285)( 42,286)( 43,288)( 44,287)( 45,282)( 46,281)( 47,283)( 48,284)
( 49,245)( 50,246)( 51,248)( 52,247)( 53,242)( 54,241)( 55,243)( 56,244)
( 57,253)( 58,254)( 59,256)( 60,255)( 61,250)( 62,249)( 63,251)( 64,252)
( 65,261)( 66,262)( 67,264)( 68,263)( 69,258)( 70,257)( 71,259)( 72,260)
( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)( 80,292)
( 81,301)( 82,302)( 83,304)( 84,303)( 85,298)( 86,297)( 87,299)( 88,300)
( 89,309)( 90,310)( 91,312)( 92,311)( 93,306)( 94,305)( 95,307)( 96,308)
( 97,341)( 98,342)( 99,344)(100,343)(101,338)(102,337)(103,339)(104,340)
(105,349)(106,350)(107,352)(108,351)(109,346)(110,345)(111,347)(112,348)
(113,357)(114,358)(115,360)(116,359)(117,354)(118,353)(119,355)(120,356)
(121,317)(122,318)(123,320)(124,319)(125,314)(126,313)(127,315)(128,316)
(129,325)(130,326)(131,328)(132,327)(133,322)(134,321)(135,323)(136,324)
(137,333)(138,334)(139,336)(140,335)(141,330)(142,329)(143,331)(144,332)
(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)(152,364)
(153,373)(154,374)(155,376)(156,375)(157,370)(158,369)(159,371)(160,372)
(161,381)(162,382)(163,384)(164,383)(165,378)(166,377)(167,379)(168,380)
(169,413)(170,414)(171,416)(172,415)(173,410)(174,409)(175,411)(176,412)
(177,421)(178,422)(179,424)(180,423)(181,418)(182,417)(183,419)(184,420)
(185,429)(186,430)(187,432)(188,431)(189,426)(190,425)(191,427)(192,428)
(193,389)(194,390)(195,392)(196,391)(197,386)(198,385)(199,387)(200,388)
(201,397)(202,398)(203,400)(204,399)(205,394)(206,393)(207,395)(208,396)
(209,405)(210,406)(211,408)(212,407)(213,402)(214,401)(215,403)(216,404);;
s1 := ( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)( 8, 30)
( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)( 16, 46)
( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)( 24, 38)
( 51, 52)( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)
( 62, 72)( 63, 69)( 64, 70)( 73,185)( 74,186)( 75,188)( 76,187)( 77,191)
( 78,192)( 79,189)( 80,190)( 81,177)( 82,178)( 83,180)( 84,179)( 85,183)
( 86,184)( 87,181)( 88,182)( 89,169)( 90,170)( 91,172)( 92,171)( 93,175)
( 94,176)( 95,173)( 96,174)( 97,161)( 98,162)( 99,164)(100,163)(101,167)
(102,168)(103,165)(104,166)(105,153)(106,154)(107,156)(108,155)(109,159)
(110,160)(111,157)(112,158)(113,145)(114,146)(115,148)(116,147)(117,151)
(118,152)(119,149)(120,150)(121,209)(122,210)(123,212)(124,211)(125,215)
(126,216)(127,213)(128,214)(129,201)(130,202)(131,204)(132,203)(133,207)
(134,208)(135,205)(136,206)(137,193)(138,194)(139,196)(140,195)(141,199)
(142,200)(143,197)(144,198)(217,242)(218,241)(219,243)(220,244)(221,248)
(222,247)(223,246)(224,245)(225,258)(226,257)(227,259)(228,260)(229,264)
(230,263)(231,262)(232,261)(233,250)(234,249)(235,251)(236,252)(237,256)
(238,255)(239,254)(240,253)(265,266)(269,272)(270,271)(273,282)(274,281)
(275,283)(276,284)(277,288)(278,287)(279,286)(280,285)(289,402)(290,401)
(291,403)(292,404)(293,408)(294,407)(295,406)(296,405)(297,394)(298,393)
(299,395)(300,396)(301,400)(302,399)(303,398)(304,397)(305,386)(306,385)
(307,387)(308,388)(309,392)(310,391)(311,390)(312,389)(313,378)(314,377)
(315,379)(316,380)(317,384)(318,383)(319,382)(320,381)(321,370)(322,369)
(323,371)(324,372)(325,376)(326,375)(327,374)(328,373)(329,362)(330,361)
(331,363)(332,364)(333,368)(334,367)(335,366)(336,365)(337,426)(338,425)
(339,427)(340,428)(341,432)(342,431)(343,430)(344,429)(345,418)(346,417)
(347,419)(348,420)(349,424)(350,423)(351,422)(352,421)(353,410)(354,409)
(355,411)(356,412)(357,416)(358,415)(359,414)(360,413);;
s2 := ( 1, 73)( 2, 74)( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)( 8, 76)
( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)( 16, 92)
( 17, 81)( 18, 82)( 19, 87)( 20, 88)( 21, 86)( 22, 85)( 23, 83)( 24, 84)
( 25, 97)( 26, 98)( 27,103)( 28,104)( 29,102)( 30,101)( 31, 99)( 32,100)
( 33,113)( 34,114)( 35,119)( 36,120)( 37,118)( 38,117)( 39,115)( 40,116)
( 41,105)( 42,106)( 43,111)( 44,112)( 45,110)( 46,109)( 47,107)( 48,108)
( 49,121)( 50,122)( 51,127)( 52,128)( 53,126)( 54,125)( 55,123)( 56,124)
( 57,137)( 58,138)( 59,143)( 60,144)( 61,142)( 62,141)( 63,139)( 64,140)
( 65,129)( 66,130)( 67,135)( 68,136)( 69,134)( 70,133)( 71,131)( 72,132)
(145,161)(146,162)(147,167)(148,168)(149,166)(150,165)(151,163)(152,164)
(155,159)(156,160)(157,158)(169,185)(170,186)(171,191)(172,192)(173,190)
(174,189)(175,187)(176,188)(179,183)(180,184)(181,182)(193,209)(194,210)
(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)(204,208)
(205,206)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)(223,292)
(224,291)(225,306)(226,305)(227,312)(228,311)(229,309)(230,310)(231,308)
(232,307)(233,298)(234,297)(235,304)(236,303)(237,301)(238,302)(239,300)
(240,299)(241,314)(242,313)(243,320)(244,319)(245,317)(246,318)(247,316)
(248,315)(249,330)(250,329)(251,336)(252,335)(253,333)(254,334)(255,332)
(256,331)(257,322)(258,321)(259,328)(260,327)(261,325)(262,326)(263,324)
(264,323)(265,338)(266,337)(267,344)(268,343)(269,341)(270,342)(271,340)
(272,339)(273,354)(274,353)(275,360)(276,359)(277,357)(278,358)(279,356)
(280,355)(281,346)(282,345)(283,352)(284,351)(285,349)(286,350)(287,348)
(288,347)(361,378)(362,377)(363,384)(364,383)(365,381)(366,382)(367,380)
(368,379)(369,370)(371,376)(372,375)(385,402)(386,401)(387,408)(388,407)
(389,405)(390,406)(391,404)(392,403)(393,394)(395,400)(396,399)(409,426)
(410,425)(411,432)(412,431)(413,429)(414,430)(415,428)(416,427)(417,418)
(419,424)(420,423);;
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*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1,221)( 2,222)( 3,224)( 4,223)( 5,218)( 6,217)( 7,219)
( 8,220)( 9,229)( 10,230)( 11,232)( 12,231)( 13,226)( 14,225)( 15,227)
( 16,228)( 17,237)( 18,238)( 19,240)( 20,239)( 21,234)( 22,233)( 23,235)
( 24,236)( 25,269)( 26,270)( 27,272)( 28,271)( 29,266)( 30,265)( 31,267)
( 32,268)( 33,277)( 34,278)( 35,280)( 36,279)( 37,274)( 38,273)( 39,275)
( 40,276)( 41,285)( 42,286)( 43,288)( 44,287)( 45,282)( 46,281)( 47,283)
( 48,284)( 49,245)( 50,246)( 51,248)( 52,247)( 53,242)( 54,241)( 55,243)
( 56,244)( 57,253)( 58,254)( 59,256)( 60,255)( 61,250)( 62,249)( 63,251)
( 64,252)( 65,261)( 66,262)( 67,264)( 68,263)( 69,258)( 70,257)( 71,259)
( 72,260)( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)
( 80,292)( 81,301)( 82,302)( 83,304)( 84,303)( 85,298)( 86,297)( 87,299)
( 88,300)( 89,309)( 90,310)( 91,312)( 92,311)( 93,306)( 94,305)( 95,307)
( 96,308)( 97,341)( 98,342)( 99,344)(100,343)(101,338)(102,337)(103,339)
(104,340)(105,349)(106,350)(107,352)(108,351)(109,346)(110,345)(111,347)
(112,348)(113,357)(114,358)(115,360)(116,359)(117,354)(118,353)(119,355)
(120,356)(121,317)(122,318)(123,320)(124,319)(125,314)(126,313)(127,315)
(128,316)(129,325)(130,326)(131,328)(132,327)(133,322)(134,321)(135,323)
(136,324)(137,333)(138,334)(139,336)(140,335)(141,330)(142,329)(143,331)
(144,332)(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)
(152,364)(153,373)(154,374)(155,376)(156,375)(157,370)(158,369)(159,371)
(160,372)(161,381)(162,382)(163,384)(164,383)(165,378)(166,377)(167,379)
(168,380)(169,413)(170,414)(171,416)(172,415)(173,410)(174,409)(175,411)
(176,412)(177,421)(178,422)(179,424)(180,423)(181,418)(182,417)(183,419)
(184,420)(185,429)(186,430)(187,432)(188,431)(189,426)(190,425)(191,427)
(192,428)(193,389)(194,390)(195,392)(196,391)(197,386)(198,385)(199,387)
(200,388)(201,397)(202,398)(203,400)(204,399)(205,394)(206,393)(207,395)
(208,396)(209,405)(210,406)(211,408)(212,407)(213,402)(214,401)(215,403)
(216,404);
s1 := Sym(432)!( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)
( 8, 30)( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)
( 16, 46)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)
( 24, 38)( 51, 52)( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)
( 61, 71)( 62, 72)( 63, 69)( 64, 70)( 73,185)( 74,186)( 75,188)( 76,187)
( 77,191)( 78,192)( 79,189)( 80,190)( 81,177)( 82,178)( 83,180)( 84,179)
( 85,183)( 86,184)( 87,181)( 88,182)( 89,169)( 90,170)( 91,172)( 92,171)
( 93,175)( 94,176)( 95,173)( 96,174)( 97,161)( 98,162)( 99,164)(100,163)
(101,167)(102,168)(103,165)(104,166)(105,153)(106,154)(107,156)(108,155)
(109,159)(110,160)(111,157)(112,158)(113,145)(114,146)(115,148)(116,147)
(117,151)(118,152)(119,149)(120,150)(121,209)(122,210)(123,212)(124,211)
(125,215)(126,216)(127,213)(128,214)(129,201)(130,202)(131,204)(132,203)
(133,207)(134,208)(135,205)(136,206)(137,193)(138,194)(139,196)(140,195)
(141,199)(142,200)(143,197)(144,198)(217,242)(218,241)(219,243)(220,244)
(221,248)(222,247)(223,246)(224,245)(225,258)(226,257)(227,259)(228,260)
(229,264)(230,263)(231,262)(232,261)(233,250)(234,249)(235,251)(236,252)
(237,256)(238,255)(239,254)(240,253)(265,266)(269,272)(270,271)(273,282)
(274,281)(275,283)(276,284)(277,288)(278,287)(279,286)(280,285)(289,402)
(290,401)(291,403)(292,404)(293,408)(294,407)(295,406)(296,405)(297,394)
(298,393)(299,395)(300,396)(301,400)(302,399)(303,398)(304,397)(305,386)
(306,385)(307,387)(308,388)(309,392)(310,391)(311,390)(312,389)(313,378)
(314,377)(315,379)(316,380)(317,384)(318,383)(319,382)(320,381)(321,370)
(322,369)(323,371)(324,372)(325,376)(326,375)(327,374)(328,373)(329,362)
(330,361)(331,363)(332,364)(333,368)(334,367)(335,366)(336,365)(337,426)
(338,425)(339,427)(340,428)(341,432)(342,431)(343,430)(344,429)(345,418)
(346,417)(347,419)(348,420)(349,424)(350,423)(351,422)(352,421)(353,410)
(354,409)(355,411)(356,412)(357,416)(358,415)(359,414)(360,413);
s2 := Sym(432)!( 1, 73)( 2, 74)( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)
( 8, 76)( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)
( 16, 92)( 17, 81)( 18, 82)( 19, 87)( 20, 88)( 21, 86)( 22, 85)( 23, 83)
( 24, 84)( 25, 97)( 26, 98)( 27,103)( 28,104)( 29,102)( 30,101)( 31, 99)
( 32,100)( 33,113)( 34,114)( 35,119)( 36,120)( 37,118)( 38,117)( 39,115)
( 40,116)( 41,105)( 42,106)( 43,111)( 44,112)( 45,110)( 46,109)( 47,107)
( 48,108)( 49,121)( 50,122)( 51,127)( 52,128)( 53,126)( 54,125)( 55,123)
( 56,124)( 57,137)( 58,138)( 59,143)( 60,144)( 61,142)( 62,141)( 63,139)
( 64,140)( 65,129)( 66,130)( 67,135)( 68,136)( 69,134)( 70,133)( 71,131)
( 72,132)(145,161)(146,162)(147,167)(148,168)(149,166)(150,165)(151,163)
(152,164)(155,159)(156,160)(157,158)(169,185)(170,186)(171,191)(172,192)
(173,190)(174,189)(175,187)(176,188)(179,183)(180,184)(181,182)(193,209)
(194,210)(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)
(204,208)(205,206)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)
(223,292)(224,291)(225,306)(226,305)(227,312)(228,311)(229,309)(230,310)
(231,308)(232,307)(233,298)(234,297)(235,304)(236,303)(237,301)(238,302)
(239,300)(240,299)(241,314)(242,313)(243,320)(244,319)(245,317)(246,318)
(247,316)(248,315)(249,330)(250,329)(251,336)(252,335)(253,333)(254,334)
(255,332)(256,331)(257,322)(258,321)(259,328)(260,327)(261,325)(262,326)
(263,324)(264,323)(265,338)(266,337)(267,344)(268,343)(269,341)(270,342)
(271,340)(272,339)(273,354)(274,353)(275,360)(276,359)(277,357)(278,358)
(279,356)(280,355)(281,346)(282,345)(283,352)(284,351)(285,349)(286,350)
(287,348)(288,347)(361,378)(362,377)(363,384)(364,383)(365,381)(366,382)
(367,380)(368,379)(369,370)(371,376)(372,375)(385,402)(386,401)(387,408)
(388,407)(389,405)(390,406)(391,404)(392,403)(393,394)(395,400)(396,399)
(409,426)(410,425)(411,432)(412,431)(413,429)(414,430)(415,428)(416,427)
(417,418)(419,424)(420,423);
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*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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 >;
References : None.
to this polytope