Polytope of Type {6,48}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,48}*1728c
if this polytope has a name.
Group : SmallGroup(1728,5302)
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}*864c
3-fold quotients : {6,48}*576c
4-fold quotients : {6,12}*432c
6-fold quotients : {6,24}*288c
8-fold quotients : {6,6}*216c
9-fold quotients : {6,16}*192
12-fold quotients : {6,12}*144c
16-fold quotients : {3,6}*108
18-fold quotients : {6,8}*96
24-fold quotients : {6,6}*72c
27-fold quotients : {2,16}*64
36-fold quotients : {6,4}*48a
48-fold quotients : {3,6}*36
54-fold quotients : {2,8}*32
72-fold quotients : {6,2}*24
108-fold quotients : {2,4}*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)
( 58, 61)( 59, 62)( 60, 63)( 64, 73)( 65, 74)( 66, 75)( 67, 79)( 68, 80)
( 69, 81)( 70, 76)( 71, 77)( 72, 78)( 85, 88)( 86, 89)( 87, 90)( 91,100)
( 92,101)( 93,102)( 94,106)( 95,107)( 96,108)( 97,103)( 98,104)( 99,105)
(112,115)(113,116)(114,117)(118,127)(119,128)(120,129)(121,133)(122,134)
(123,135)(124,130)(125,131)(126,132)(139,142)(140,143)(141,144)(145,154)
(146,155)(147,156)(148,160)(149,161)(150,162)(151,157)(152,158)(153,159)
(166,169)(167,170)(168,171)(172,181)(173,182)(174,183)(175,187)(176,188)
(177,189)(178,184)(179,185)(180,186)(193,196)(194,197)(195,198)(199,208)
(200,209)(201,210)(202,214)(203,215)(204,216)(205,211)(206,212)(207,213)
(220,223)(221,224)(222,225)(226,235)(227,236)(228,237)(229,241)(230,242)
(231,243)(232,238)(233,239)(234,240)(247,250)(248,251)(249,252)(253,262)
(254,263)(255,264)(256,268)(257,269)(258,270)(259,265)(260,266)(261,267)
(274,277)(275,278)(276,279)(280,289)(281,290)(282,291)(283,295)(284,296)
(285,297)(286,292)(287,293)(288,294)(301,304)(302,305)(303,306)(307,316)
(308,317)(309,318)(310,322)(311,323)(312,324)(313,319)(314,320)(315,321)
(328,331)(329,332)(330,333)(334,343)(335,344)(336,345)(337,349)(338,350)
(339,351)(340,346)(341,347)(342,348)(355,358)(356,359)(357,360)(361,370)
(362,371)(363,372)(364,376)(365,377)(366,378)(367,373)(368,374)(369,375)
(382,385)(383,386)(384,387)(388,397)(389,398)(390,399)(391,403)(392,404)
(393,405)(394,400)(395,401)(396,402)(409,412)(410,413)(411,414)(415,424)
(416,425)(417,426)(418,430)(419,431)(420,432)(421,427)(422,428)(423,429);;
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)
( 55, 82)( 56, 84)( 57, 83)( 58, 85)( 59, 87)( 60, 86)( 61, 88)( 62, 90)
( 63, 89)( 64,100)( 65,102)( 66,101)( 67,103)( 68,105)( 69,104)( 70,106)
( 71,108)( 72,107)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)( 78, 95)
( 79, 97)( 80, 99)( 81, 98)(109,163)(110,165)(111,164)(112,166)(113,168)
(114,167)(115,169)(116,171)(117,170)(118,181)(119,183)(120,182)(121,184)
(122,186)(123,185)(124,187)(125,189)(126,188)(127,172)(128,174)(129,173)
(130,175)(131,177)(132,176)(133,178)(134,180)(135,179)(136,190)(137,192)
(138,191)(139,193)(140,195)(141,194)(142,196)(143,198)(144,197)(145,208)
(146,210)(147,209)(148,211)(149,213)(150,212)(151,214)(152,216)(153,215)
(154,199)(155,201)(156,200)(157,202)(158,204)(159,203)(160,205)(161,207)
(162,206)(217,325)(218,327)(219,326)(220,328)(221,330)(222,329)(223,331)
(224,333)(225,332)(226,343)(227,345)(228,344)(229,346)(230,348)(231,347)
(232,349)(233,351)(234,350)(235,334)(236,336)(237,335)(238,337)(239,339)
(240,338)(241,340)(242,342)(243,341)(244,352)(245,354)(246,353)(247,355)
(248,357)(249,356)(250,358)(251,360)(252,359)(253,370)(254,372)(255,371)
(256,373)(257,375)(258,374)(259,376)(260,378)(261,377)(262,361)(263,363)
(264,362)(265,364)(266,366)(267,365)(268,367)(269,369)(270,368)(271,406)
(272,408)(273,407)(274,409)(275,411)(276,410)(277,412)(278,414)(279,413)
(280,424)(281,426)(282,425)(283,427)(284,429)(285,428)(286,430)(287,432)
(288,431)(289,415)(290,417)(291,416)(292,418)(293,420)(294,419)(295,421)
(296,423)(297,422)(298,379)(299,381)(300,380)(301,382)(302,384)(303,383)
(304,385)(305,387)(306,386)(307,397)(308,399)(309,398)(310,400)(311,402)
(312,401)(313,403)(314,405)(315,404)(316,388)(317,390)(318,389)(319,391)
(320,393)(321,392)(322,394)(323,396)(324,395);;
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,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*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)( 58, 61)( 59, 62)( 60, 63)( 64, 73)( 65, 74)( 66, 75)( 67, 79)
( 68, 80)( 69, 81)( 70, 76)( 71, 77)( 72, 78)( 85, 88)( 86, 89)( 87, 90)
( 91,100)( 92,101)( 93,102)( 94,106)( 95,107)( 96,108)( 97,103)( 98,104)
( 99,105)(112,115)(113,116)(114,117)(118,127)(119,128)(120,129)(121,133)
(122,134)(123,135)(124,130)(125,131)(126,132)(139,142)(140,143)(141,144)
(145,154)(146,155)(147,156)(148,160)(149,161)(150,162)(151,157)(152,158)
(153,159)(166,169)(167,170)(168,171)(172,181)(173,182)(174,183)(175,187)
(176,188)(177,189)(178,184)(179,185)(180,186)(193,196)(194,197)(195,198)
(199,208)(200,209)(201,210)(202,214)(203,215)(204,216)(205,211)(206,212)
(207,213)(220,223)(221,224)(222,225)(226,235)(227,236)(228,237)(229,241)
(230,242)(231,243)(232,238)(233,239)(234,240)(247,250)(248,251)(249,252)
(253,262)(254,263)(255,264)(256,268)(257,269)(258,270)(259,265)(260,266)
(261,267)(274,277)(275,278)(276,279)(280,289)(281,290)(282,291)(283,295)
(284,296)(285,297)(286,292)(287,293)(288,294)(301,304)(302,305)(303,306)
(307,316)(308,317)(309,318)(310,322)(311,323)(312,324)(313,319)(314,320)
(315,321)(328,331)(329,332)(330,333)(334,343)(335,344)(336,345)(337,349)
(338,350)(339,351)(340,346)(341,347)(342,348)(355,358)(356,359)(357,360)
(361,370)(362,371)(363,372)(364,376)(365,377)(366,378)(367,373)(368,374)
(369,375)(382,385)(383,386)(384,387)(388,397)(389,398)(390,399)(391,403)
(392,404)(393,405)(394,400)(395,401)(396,402)(409,412)(410,413)(411,414)
(415,424)(416,425)(417,426)(418,430)(419,431)(420,432)(421,427)(422,428)
(423,429);
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)( 55, 82)( 56, 84)( 57, 83)( 58, 85)( 59, 87)( 60, 86)( 61, 88)
( 62, 90)( 63, 89)( 64,100)( 65,102)( 66,101)( 67,103)( 68,105)( 69,104)
( 70,106)( 71,108)( 72,107)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)
( 78, 95)( 79, 97)( 80, 99)( 81, 98)(109,163)(110,165)(111,164)(112,166)
(113,168)(114,167)(115,169)(116,171)(117,170)(118,181)(119,183)(120,182)
(121,184)(122,186)(123,185)(124,187)(125,189)(126,188)(127,172)(128,174)
(129,173)(130,175)(131,177)(132,176)(133,178)(134,180)(135,179)(136,190)
(137,192)(138,191)(139,193)(140,195)(141,194)(142,196)(143,198)(144,197)
(145,208)(146,210)(147,209)(148,211)(149,213)(150,212)(151,214)(152,216)
(153,215)(154,199)(155,201)(156,200)(157,202)(158,204)(159,203)(160,205)
(161,207)(162,206)(217,325)(218,327)(219,326)(220,328)(221,330)(222,329)
(223,331)(224,333)(225,332)(226,343)(227,345)(228,344)(229,346)(230,348)
(231,347)(232,349)(233,351)(234,350)(235,334)(236,336)(237,335)(238,337)
(239,339)(240,338)(241,340)(242,342)(243,341)(244,352)(245,354)(246,353)
(247,355)(248,357)(249,356)(250,358)(251,360)(252,359)(253,370)(254,372)
(255,371)(256,373)(257,375)(258,374)(259,376)(260,378)(261,377)(262,361)
(263,363)(264,362)(265,364)(266,366)(267,365)(268,367)(269,369)(270,368)
(271,406)(272,408)(273,407)(274,409)(275,411)(276,410)(277,412)(278,414)
(279,413)(280,424)(281,426)(282,425)(283,427)(284,429)(285,428)(286,430)
(287,432)(288,431)(289,415)(290,417)(291,416)(292,418)(293,420)(294,419)
(295,421)(296,423)(297,422)(298,379)(299,381)(300,380)(301,382)(302,384)
(303,383)(304,385)(305,387)(306,386)(307,397)(308,399)(309,398)(310,400)
(311,402)(312,401)(313,403)(314,405)(315,404)(316,388)(317,390)(318,389)
(319,391)(320,393)(321,392)(322,394)(323,396)(324,395);
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,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 >;
References : None.
to this polytope