Polytope of Type {48,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6}*1728c
if this polytope has a name.
Group : SmallGroup(1728,5302)
Rank : 3
Schlafli Type : {48,6}
Number of vertices, edges, etc : 144, 432, 18
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,6}*864c
   3-fold quotients : {48,6}*576c
   4-fold quotients : {12,6}*432c
   6-fold quotients : {24,6}*288c
   8-fold quotients : {6,6}*216a
   9-fold quotients : {16,6}*192
   12-fold quotients : {12,6}*144c
   16-fold quotients : {6,3}*108
   18-fold quotients : {8,6}*96
   24-fold quotients : {6,6}*72b
   27-fold quotients : {16,2}*64
   36-fold quotients : {4,6}*48a
   48-fold quotients : {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 := (  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);;
s1 := (  1,226)(  2,227)(  3,228)(  4,234)(  5,232)(  6,233)(  7,230)(  8,231)
(  9,229)( 10,217)( 11,218)( 12,219)( 13,225)( 14,223)( 15,224)( 16,221)
( 17,222)( 18,220)( 19,235)( 20,236)( 21,237)( 22,243)( 23,241)( 24,242)
( 25,239)( 26,240)( 27,238)( 28,253)( 29,254)( 30,255)( 31,261)( 32,259)
( 33,260)( 34,257)( 35,258)( 36,256)( 37,244)( 38,245)( 39,246)( 40,252)
( 41,250)( 42,251)( 43,248)( 44,249)( 45,247)( 46,262)( 47,263)( 48,264)
( 49,270)( 50,268)( 51,269)( 52,266)( 53,267)( 54,265)( 55,307)( 56,308)
( 57,309)( 58,315)( 59,313)( 60,314)( 61,311)( 62,312)( 63,310)( 64,298)
( 65,299)( 66,300)( 67,306)( 68,304)( 69,305)( 70,302)( 71,303)( 72,301)
( 73,316)( 74,317)( 75,318)( 76,324)( 77,322)( 78,323)( 79,320)( 80,321)
( 81,319)( 82,280)( 83,281)( 84,282)( 85,288)( 86,286)( 87,287)( 88,284)
( 89,285)( 90,283)( 91,271)( 92,272)( 93,273)( 94,279)( 95,277)( 96,278)
( 97,275)( 98,276)( 99,274)(100,289)(101,290)(102,291)(103,297)(104,295)
(105,296)(106,293)(107,294)(108,292)(109,388)(110,389)(111,390)(112,396)
(113,394)(114,395)(115,392)(116,393)(117,391)(118,379)(119,380)(120,381)
(121,387)(122,385)(123,386)(124,383)(125,384)(126,382)(127,397)(128,398)
(129,399)(130,405)(131,403)(132,404)(133,401)(134,402)(135,400)(136,415)
(137,416)(138,417)(139,423)(140,421)(141,422)(142,419)(143,420)(144,418)
(145,406)(146,407)(147,408)(148,414)(149,412)(150,413)(151,410)(152,411)
(153,409)(154,424)(155,425)(156,426)(157,432)(158,430)(159,431)(160,428)
(161,429)(162,427)(163,334)(164,335)(165,336)(166,342)(167,340)(168,341)
(169,338)(170,339)(171,337)(172,325)(173,326)(174,327)(175,333)(176,331)
(177,332)(178,329)(179,330)(180,328)(181,343)(182,344)(183,345)(184,351)
(185,349)(186,350)(187,347)(188,348)(189,346)(190,361)(191,362)(192,363)
(193,369)(194,367)(195,368)(196,365)(197,366)(198,364)(199,352)(200,353)
(201,354)(202,360)(203,358)(204,359)(205,356)(206,357)(207,355)(208,370)
(209,371)(210,372)(211,378)(212,376)(213,377)(214,374)(215,375)(216,373);;
s2 := (  1,  4)(  2,  5)(  3,  6)( 10, 22)( 11, 23)( 12, 24)( 13, 19)( 14, 20)
( 15, 21)( 16, 25)( 17, 26)( 18, 27)( 28, 31)( 29, 32)( 30, 33)( 37, 49)
( 38, 50)( 39, 51)( 40, 46)( 41, 47)( 42, 48)( 43, 52)( 44, 53)( 45, 54)
( 55, 58)( 56, 59)( 57, 60)( 64, 76)( 65, 77)( 66, 78)( 67, 73)( 68, 74)
( 69, 75)( 70, 79)( 71, 80)( 72, 81)( 82, 85)( 83, 86)( 84, 87)( 91,103)
( 92,104)( 93,105)( 94,100)( 95,101)( 96,102)( 97,106)( 98,107)( 99,108)
(109,112)(110,113)(111,114)(118,130)(119,131)(120,132)(121,127)(122,128)
(123,129)(124,133)(125,134)(126,135)(136,139)(137,140)(138,141)(145,157)
(146,158)(147,159)(148,154)(149,155)(150,156)(151,160)(152,161)(153,162)
(163,166)(164,167)(165,168)(172,184)(173,185)(174,186)(175,181)(176,182)
(177,183)(178,187)(179,188)(180,189)(190,193)(191,194)(192,195)(199,211)
(200,212)(201,213)(202,208)(203,209)(204,210)(205,214)(206,215)(207,216)
(217,220)(218,221)(219,222)(226,238)(227,239)(228,240)(229,235)(230,236)
(231,237)(232,241)(233,242)(234,243)(244,247)(245,248)(246,249)(253,265)
(254,266)(255,267)(256,262)(257,263)(258,264)(259,268)(260,269)(261,270)
(271,274)(272,275)(273,276)(280,292)(281,293)(282,294)(283,289)(284,290)
(285,291)(286,295)(287,296)(288,297)(298,301)(299,302)(300,303)(307,319)
(308,320)(309,321)(310,316)(311,317)(312,318)(313,322)(314,323)(315,324)
(325,328)(326,329)(327,330)(334,346)(335,347)(336,348)(337,343)(338,344)
(339,345)(340,349)(341,350)(342,351)(352,355)(353,356)(354,357)(361,373)
(362,374)(363,375)(364,370)(365,371)(366,372)(367,376)(368,377)(369,378)
(379,382)(380,383)(381,384)(388,400)(389,401)(390,402)(391,397)(392,398)
(393,399)(394,403)(395,404)(396,405)(406,409)(407,410)(408,411)(415,427)
(416,428)(417,429)(418,424)(419,425)(420,426)(421,430)(422,431)(423,432);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
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)( 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);
s1 := Sym(432)!(  1,226)(  2,227)(  3,228)(  4,234)(  5,232)(  6,233)(  7,230)
(  8,231)(  9,229)( 10,217)( 11,218)( 12,219)( 13,225)( 14,223)( 15,224)
( 16,221)( 17,222)( 18,220)( 19,235)( 20,236)( 21,237)( 22,243)( 23,241)
( 24,242)( 25,239)( 26,240)( 27,238)( 28,253)( 29,254)( 30,255)( 31,261)
( 32,259)( 33,260)( 34,257)( 35,258)( 36,256)( 37,244)( 38,245)( 39,246)
( 40,252)( 41,250)( 42,251)( 43,248)( 44,249)( 45,247)( 46,262)( 47,263)
( 48,264)( 49,270)( 50,268)( 51,269)( 52,266)( 53,267)( 54,265)( 55,307)
( 56,308)( 57,309)( 58,315)( 59,313)( 60,314)( 61,311)( 62,312)( 63,310)
( 64,298)( 65,299)( 66,300)( 67,306)( 68,304)( 69,305)( 70,302)( 71,303)
( 72,301)( 73,316)( 74,317)( 75,318)( 76,324)( 77,322)( 78,323)( 79,320)
( 80,321)( 81,319)( 82,280)( 83,281)( 84,282)( 85,288)( 86,286)( 87,287)
( 88,284)( 89,285)( 90,283)( 91,271)( 92,272)( 93,273)( 94,279)( 95,277)
( 96,278)( 97,275)( 98,276)( 99,274)(100,289)(101,290)(102,291)(103,297)
(104,295)(105,296)(106,293)(107,294)(108,292)(109,388)(110,389)(111,390)
(112,396)(113,394)(114,395)(115,392)(116,393)(117,391)(118,379)(119,380)
(120,381)(121,387)(122,385)(123,386)(124,383)(125,384)(126,382)(127,397)
(128,398)(129,399)(130,405)(131,403)(132,404)(133,401)(134,402)(135,400)
(136,415)(137,416)(138,417)(139,423)(140,421)(141,422)(142,419)(143,420)
(144,418)(145,406)(146,407)(147,408)(148,414)(149,412)(150,413)(151,410)
(152,411)(153,409)(154,424)(155,425)(156,426)(157,432)(158,430)(159,431)
(160,428)(161,429)(162,427)(163,334)(164,335)(165,336)(166,342)(167,340)
(168,341)(169,338)(170,339)(171,337)(172,325)(173,326)(174,327)(175,333)
(176,331)(177,332)(178,329)(179,330)(180,328)(181,343)(182,344)(183,345)
(184,351)(185,349)(186,350)(187,347)(188,348)(189,346)(190,361)(191,362)
(192,363)(193,369)(194,367)(195,368)(196,365)(197,366)(198,364)(199,352)
(200,353)(201,354)(202,360)(203,358)(204,359)(205,356)(206,357)(207,355)
(208,370)(209,371)(210,372)(211,378)(212,376)(213,377)(214,374)(215,375)
(216,373);
s2 := Sym(432)!(  1,  4)(  2,  5)(  3,  6)( 10, 22)( 11, 23)( 12, 24)( 13, 19)
( 14, 20)( 15, 21)( 16, 25)( 17, 26)( 18, 27)( 28, 31)( 29, 32)( 30, 33)
( 37, 49)( 38, 50)( 39, 51)( 40, 46)( 41, 47)( 42, 48)( 43, 52)( 44, 53)
( 45, 54)( 55, 58)( 56, 59)( 57, 60)( 64, 76)( 65, 77)( 66, 78)( 67, 73)
( 68, 74)( 69, 75)( 70, 79)( 71, 80)( 72, 81)( 82, 85)( 83, 86)( 84, 87)
( 91,103)( 92,104)( 93,105)( 94,100)( 95,101)( 96,102)( 97,106)( 98,107)
( 99,108)(109,112)(110,113)(111,114)(118,130)(119,131)(120,132)(121,127)
(122,128)(123,129)(124,133)(125,134)(126,135)(136,139)(137,140)(138,141)
(145,157)(146,158)(147,159)(148,154)(149,155)(150,156)(151,160)(152,161)
(153,162)(163,166)(164,167)(165,168)(172,184)(173,185)(174,186)(175,181)
(176,182)(177,183)(178,187)(179,188)(180,189)(190,193)(191,194)(192,195)
(199,211)(200,212)(201,213)(202,208)(203,209)(204,210)(205,214)(206,215)
(207,216)(217,220)(218,221)(219,222)(226,238)(227,239)(228,240)(229,235)
(230,236)(231,237)(232,241)(233,242)(234,243)(244,247)(245,248)(246,249)
(253,265)(254,266)(255,267)(256,262)(257,263)(258,264)(259,268)(260,269)
(261,270)(271,274)(272,275)(273,276)(280,292)(281,293)(282,294)(283,289)
(284,290)(285,291)(286,295)(287,296)(288,297)(298,301)(299,302)(300,303)
(307,319)(308,320)(309,321)(310,316)(311,317)(312,318)(313,322)(314,323)
(315,324)(325,328)(326,329)(327,330)(334,346)(335,347)(336,348)(337,343)
(338,344)(339,345)(340,349)(341,350)(342,351)(352,355)(353,356)(354,357)
(361,373)(362,374)(363,375)(364,370)(365,371)(366,372)(367,376)(368,377)
(369,378)(379,382)(380,383)(381,384)(388,400)(389,401)(390,402)(391,397)
(392,398)(393,399)(394,403)(395,404)(396,405)(406,409)(407,410)(408,411)
(415,427)(416,428)(417,429)(418,424)(419,425)(420,426)(421,430)(422,431)
(423,432);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope