Polytope of Type {6,48}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,48}*1728a
if this polytope has a name.
Group : SmallGroup(1728,3073)
Rank : 3
Schlafli Type : {6,48}
Number of vertices, edges, etc : 18, 432, 144
Order of s0s1s2 : 48
Order of s0s1s2s1 : 6
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 : {6,24}*864a
3-fold quotients : {6,48}*576b
4-fold quotients : {6,12}*432a
6-fold quotients : {6,24}*288b
8-fold quotients : {6,6}*216a
9-fold quotients : {2,48}*192
12-fold quotients : {6,12}*144b
16-fold quotients : {6,3}*108
18-fold quotients : {2,24}*96
24-fold quotients : {6,6}*72b
27-fold quotients : {2,16}*64
36-fold quotients : {2,12}*48
48-fold quotients : {6,3}*36
54-fold quotients : {2,8}*32
72-fold quotients : {2,6}*24
108-fold quotients : {2,4}*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 := ( 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);;
s1 := ( 1, 10)( 2, 11)( 3, 12)( 4, 18)( 5, 16)( 6, 17)( 7, 14)( 8, 15)
( 9, 13)( 22, 27)( 23, 25)( 24, 26)( 28, 37)( 29, 38)( 30, 39)( 31, 45)
( 32, 43)( 33, 44)( 34, 41)( 35, 42)( 36, 40)( 49, 54)( 50, 52)( 51, 53)
( 55, 91)( 56, 92)( 57, 93)( 58, 99)( 59, 97)( 60, 98)( 61, 95)( 62, 96)
( 63, 94)( 64, 82)( 65, 83)( 66, 84)( 67, 90)( 68, 88)( 69, 89)( 70, 86)
( 71, 87)( 72, 85)( 73,100)( 74,101)( 75,102)( 76,108)( 77,106)( 78,107)
( 79,104)( 80,105)( 81,103)(109,172)(110,173)(111,174)(112,180)(113,178)
(114,179)(115,176)(116,177)(117,175)(118,163)(119,164)(120,165)(121,171)
(122,169)(123,170)(124,167)(125,168)(126,166)(127,181)(128,182)(129,183)
(130,189)(131,187)(132,188)(133,185)(134,186)(135,184)(136,199)(137,200)
(138,201)(139,207)(140,205)(141,206)(142,203)(143,204)(144,202)(145,190)
(146,191)(147,192)(148,198)(149,196)(150,197)(151,194)(152,195)(153,193)
(154,208)(155,209)(156,210)(157,216)(158,214)(159,215)(160,212)(161,213)
(162,211)(217,334)(218,335)(219,336)(220,342)(221,340)(222,341)(223,338)
(224,339)(225,337)(226,325)(227,326)(228,327)(229,333)(230,331)(231,332)
(232,329)(233,330)(234,328)(235,343)(236,344)(237,345)(238,351)(239,349)
(240,350)(241,347)(242,348)(243,346)(244,361)(245,362)(246,363)(247,369)
(248,367)(249,368)(250,365)(251,366)(252,364)(253,352)(254,353)(255,354)
(256,360)(257,358)(258,359)(259,356)(260,357)(261,355)(262,370)(263,371)
(264,372)(265,378)(266,376)(267,377)(268,374)(269,375)(270,373)(271,415)
(272,416)(273,417)(274,423)(275,421)(276,422)(277,419)(278,420)(279,418)
(280,406)(281,407)(282,408)(283,414)(284,412)(285,413)(286,410)(287,411)
(288,409)(289,424)(290,425)(291,426)(292,432)(293,430)(294,431)(295,428)
(296,429)(297,427)(298,388)(299,389)(300,390)(301,396)(302,394)(303,395)
(304,392)(305,393)(306,391)(307,379)(308,380)(309,381)(310,387)(311,385)
(312,386)(313,383)(314,384)(315,382)(316,397)(317,398)(318,399)(319,405)
(320,403)(321,404)(322,401)(323,402)(324,400);;
s2 := ( 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);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*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, 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);
s1 := Sym(432)!( 1, 10)( 2, 11)( 3, 12)( 4, 18)( 5, 16)( 6, 17)( 7, 14)
( 8, 15)( 9, 13)( 22, 27)( 23, 25)( 24, 26)( 28, 37)( 29, 38)( 30, 39)
( 31, 45)( 32, 43)( 33, 44)( 34, 41)( 35, 42)( 36, 40)( 49, 54)( 50, 52)
( 51, 53)( 55, 91)( 56, 92)( 57, 93)( 58, 99)( 59, 97)( 60, 98)( 61, 95)
( 62, 96)( 63, 94)( 64, 82)( 65, 83)( 66, 84)( 67, 90)( 68, 88)( 69, 89)
( 70, 86)( 71, 87)( 72, 85)( 73,100)( 74,101)( 75,102)( 76,108)( 77,106)
( 78,107)( 79,104)( 80,105)( 81,103)(109,172)(110,173)(111,174)(112,180)
(113,178)(114,179)(115,176)(116,177)(117,175)(118,163)(119,164)(120,165)
(121,171)(122,169)(123,170)(124,167)(125,168)(126,166)(127,181)(128,182)
(129,183)(130,189)(131,187)(132,188)(133,185)(134,186)(135,184)(136,199)
(137,200)(138,201)(139,207)(140,205)(141,206)(142,203)(143,204)(144,202)
(145,190)(146,191)(147,192)(148,198)(149,196)(150,197)(151,194)(152,195)
(153,193)(154,208)(155,209)(156,210)(157,216)(158,214)(159,215)(160,212)
(161,213)(162,211)(217,334)(218,335)(219,336)(220,342)(221,340)(222,341)
(223,338)(224,339)(225,337)(226,325)(227,326)(228,327)(229,333)(230,331)
(231,332)(232,329)(233,330)(234,328)(235,343)(236,344)(237,345)(238,351)
(239,349)(240,350)(241,347)(242,348)(243,346)(244,361)(245,362)(246,363)
(247,369)(248,367)(249,368)(250,365)(251,366)(252,364)(253,352)(254,353)
(255,354)(256,360)(257,358)(258,359)(259,356)(260,357)(261,355)(262,370)
(263,371)(264,372)(265,378)(266,376)(267,377)(268,374)(269,375)(270,373)
(271,415)(272,416)(273,417)(274,423)(275,421)(276,422)(277,419)(278,420)
(279,418)(280,406)(281,407)(282,408)(283,414)(284,412)(285,413)(286,410)
(287,411)(288,409)(289,424)(290,425)(291,426)(292,432)(293,430)(294,431)
(295,428)(296,429)(297,427)(298,388)(299,389)(300,390)(301,396)(302,394)
(303,395)(304,392)(305,393)(306,391)(307,379)(308,380)(309,381)(310,387)
(311,385)(312,386)(313,383)(314,384)(315,382)(316,397)(317,398)(318,399)
(319,405)(320,403)(321,404)(322,401)(323,402)(324,400);
s2 := 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);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*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