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Polytope of Type {384}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {384}*768
Also Known As : 384-gon, {384}. if this polytope has another name.
Group : SmallGroup(768,57481)
Rank : 2
Schlafli Type : {384}
Number of vertices, edges, etc : 384, 384
Order of s0s1 : 384
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
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 : {192}*384
   3-fold quotients : {128}*256
   4-fold quotients : {96}*192
   6-fold quotients : {64}*128
   8-fold quotients : {48}*96
   12-fold quotients : {32}*64
   16-fold quotients : {24}*48
   24-fold quotients : {16}*32
   32-fold quotients : {12}*24
   48-fold quotients : {8}*16
   64-fold quotients : {6}*12
   96-fold quotients : {4}*8
   128-fold quotients : {3}*6
   192-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  3)(  5,  6)(  7, 10)(  8, 12)(  9, 11)( 13, 19)( 14, 21)( 15, 20)
( 16, 22)( 17, 24)( 18, 23)( 25, 37)( 26, 39)( 27, 38)( 28, 40)( 29, 42)
( 30, 41)( 31, 46)( 32, 48)( 33, 47)( 34, 43)( 35, 45)( 36, 44)( 49, 73)
( 50, 75)( 51, 74)( 52, 76)( 53, 78)( 54, 77)( 55, 82)( 56, 84)( 57, 83)
( 58, 79)( 59, 81)( 60, 80)( 61, 91)( 62, 93)( 63, 92)( 64, 94)( 65, 96)
( 66, 95)( 67, 85)( 68, 87)( 69, 86)( 70, 88)( 71, 90)( 72, 89)( 97,145)
( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,154)(104,156)(105,155)
(106,151)(107,153)(108,152)(109,163)(110,165)(111,164)(112,166)(113,168)
(114,167)(115,157)(116,159)(117,158)(118,160)(119,162)(120,161)(121,181)
(122,183)(123,182)(124,184)(125,186)(126,185)(127,190)(128,192)(129,191)
(130,187)(131,189)(132,188)(133,169)(134,171)(135,170)(136,172)(137,174)
(138,173)(139,178)(140,180)(141,179)(142,175)(143,177)(144,176)(193,289)
(194,291)(195,290)(196,292)(197,294)(198,293)(199,298)(200,300)(201,299)
(202,295)(203,297)(204,296)(205,307)(206,309)(207,308)(208,310)(209,312)
(210,311)(211,301)(212,303)(213,302)(214,304)(215,306)(216,305)(217,325)
(218,327)(219,326)(220,328)(221,330)(222,329)(223,334)(224,336)(225,335)
(226,331)(227,333)(228,332)(229,313)(230,315)(231,314)(232,316)(233,318)
(234,317)(235,322)(236,324)(237,323)(238,319)(239,321)(240,320)(241,361)
(242,363)(243,362)(244,364)(245,366)(246,365)(247,370)(248,372)(249,371)
(250,367)(251,369)(252,368)(253,379)(254,381)(255,380)(256,382)(257,384)
(258,383)(259,373)(260,375)(261,374)(262,376)(263,378)(264,377)(265,337)
(266,339)(267,338)(268,340)(269,342)(270,341)(271,346)(272,348)(273,347)
(274,343)(275,345)(276,344)(277,355)(278,357)(279,356)(280,358)(281,360)
(282,359)(283,349)(284,351)(285,350)(286,352)(287,354)(288,353);;
s1 := (  1,195)(  2,194)(  3,193)(  4,198)(  5,197)(  6,196)(  7,204)(  8,203)
(  9,202)( 10,201)( 11,200)( 12,199)( 13,213)( 14,212)( 15,211)( 16,216)
( 17,215)( 18,214)( 19,207)( 20,206)( 21,205)( 22,210)( 23,209)( 24,208)
( 25,231)( 26,230)( 27,229)( 28,234)( 29,233)( 30,232)( 31,240)( 32,239)
( 33,238)( 34,237)( 35,236)( 36,235)( 37,219)( 38,218)( 39,217)( 40,222)
( 41,221)( 42,220)( 43,228)( 44,227)( 45,226)( 46,225)( 47,224)( 48,223)
( 49,267)( 50,266)( 51,265)( 52,270)( 53,269)( 54,268)( 55,276)( 56,275)
( 57,274)( 58,273)( 59,272)( 60,271)( 61,285)( 62,284)( 63,283)( 64,288)
( 65,287)( 66,286)( 67,279)( 68,278)( 69,277)( 70,282)( 71,281)( 72,280)
( 73,243)( 74,242)( 75,241)( 76,246)( 77,245)( 78,244)( 79,252)( 80,251)
( 81,250)( 82,249)( 83,248)( 84,247)( 85,261)( 86,260)( 87,259)( 88,264)
( 89,263)( 90,262)( 91,255)( 92,254)( 93,253)( 94,258)( 95,257)( 96,256)
( 97,339)( 98,338)( 99,337)(100,342)(101,341)(102,340)(103,348)(104,347)
(105,346)(106,345)(107,344)(108,343)(109,357)(110,356)(111,355)(112,360)
(113,359)(114,358)(115,351)(116,350)(117,349)(118,354)(119,353)(120,352)
(121,375)(122,374)(123,373)(124,378)(125,377)(126,376)(127,384)(128,383)
(129,382)(130,381)(131,380)(132,379)(133,363)(134,362)(135,361)(136,366)
(137,365)(138,364)(139,372)(140,371)(141,370)(142,369)(143,368)(144,367)
(145,291)(146,290)(147,289)(148,294)(149,293)(150,292)(151,300)(152,299)
(153,298)(154,297)(155,296)(156,295)(157,309)(158,308)(159,307)(160,312)
(161,311)(162,310)(163,303)(164,302)(165,301)(166,306)(167,305)(168,304)
(169,327)(170,326)(171,325)(172,330)(173,329)(174,328)(175,336)(176,335)
(177,334)(178,333)(179,332)(180,331)(181,315)(182,314)(183,313)(184,318)
(185,317)(186,316)(187,324)(188,323)(189,322)(190,321)(191,320)(192,319);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(384)!(  2,  3)(  5,  6)(  7, 10)(  8, 12)(  9, 11)( 13, 19)( 14, 21)
( 15, 20)( 16, 22)( 17, 24)( 18, 23)( 25, 37)( 26, 39)( 27, 38)( 28, 40)
( 29, 42)( 30, 41)( 31, 46)( 32, 48)( 33, 47)( 34, 43)( 35, 45)( 36, 44)
( 49, 73)( 50, 75)( 51, 74)( 52, 76)( 53, 78)( 54, 77)( 55, 82)( 56, 84)
( 57, 83)( 58, 79)( 59, 81)( 60, 80)( 61, 91)( 62, 93)( 63, 92)( 64, 94)
( 65, 96)( 66, 95)( 67, 85)( 68, 87)( 69, 86)( 70, 88)( 71, 90)( 72, 89)
( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,154)(104,156)
(105,155)(106,151)(107,153)(108,152)(109,163)(110,165)(111,164)(112,166)
(113,168)(114,167)(115,157)(116,159)(117,158)(118,160)(119,162)(120,161)
(121,181)(122,183)(123,182)(124,184)(125,186)(126,185)(127,190)(128,192)
(129,191)(130,187)(131,189)(132,188)(133,169)(134,171)(135,170)(136,172)
(137,174)(138,173)(139,178)(140,180)(141,179)(142,175)(143,177)(144,176)
(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,298)(200,300)
(201,299)(202,295)(203,297)(204,296)(205,307)(206,309)(207,308)(208,310)
(209,312)(210,311)(211,301)(212,303)(213,302)(214,304)(215,306)(216,305)
(217,325)(218,327)(219,326)(220,328)(221,330)(222,329)(223,334)(224,336)
(225,335)(226,331)(227,333)(228,332)(229,313)(230,315)(231,314)(232,316)
(233,318)(234,317)(235,322)(236,324)(237,323)(238,319)(239,321)(240,320)
(241,361)(242,363)(243,362)(244,364)(245,366)(246,365)(247,370)(248,372)
(249,371)(250,367)(251,369)(252,368)(253,379)(254,381)(255,380)(256,382)
(257,384)(258,383)(259,373)(260,375)(261,374)(262,376)(263,378)(264,377)
(265,337)(266,339)(267,338)(268,340)(269,342)(270,341)(271,346)(272,348)
(273,347)(274,343)(275,345)(276,344)(277,355)(278,357)(279,356)(280,358)
(281,360)(282,359)(283,349)(284,351)(285,350)(286,352)(287,354)(288,353);
s1 := Sym(384)!(  1,195)(  2,194)(  3,193)(  4,198)(  5,197)(  6,196)(  7,204)
(  8,203)(  9,202)( 10,201)( 11,200)( 12,199)( 13,213)( 14,212)( 15,211)
( 16,216)( 17,215)( 18,214)( 19,207)( 20,206)( 21,205)( 22,210)( 23,209)
( 24,208)( 25,231)( 26,230)( 27,229)( 28,234)( 29,233)( 30,232)( 31,240)
( 32,239)( 33,238)( 34,237)( 35,236)( 36,235)( 37,219)( 38,218)( 39,217)
( 40,222)( 41,221)( 42,220)( 43,228)( 44,227)( 45,226)( 46,225)( 47,224)
( 48,223)( 49,267)( 50,266)( 51,265)( 52,270)( 53,269)( 54,268)( 55,276)
( 56,275)( 57,274)( 58,273)( 59,272)( 60,271)( 61,285)( 62,284)( 63,283)
( 64,288)( 65,287)( 66,286)( 67,279)( 68,278)( 69,277)( 70,282)( 71,281)
( 72,280)( 73,243)( 74,242)( 75,241)( 76,246)( 77,245)( 78,244)( 79,252)
( 80,251)( 81,250)( 82,249)( 83,248)( 84,247)( 85,261)( 86,260)( 87,259)
( 88,264)( 89,263)( 90,262)( 91,255)( 92,254)( 93,253)( 94,258)( 95,257)
( 96,256)( 97,339)( 98,338)( 99,337)(100,342)(101,341)(102,340)(103,348)
(104,347)(105,346)(106,345)(107,344)(108,343)(109,357)(110,356)(111,355)
(112,360)(113,359)(114,358)(115,351)(116,350)(117,349)(118,354)(119,353)
(120,352)(121,375)(122,374)(123,373)(124,378)(125,377)(126,376)(127,384)
(128,383)(129,382)(130,381)(131,380)(132,379)(133,363)(134,362)(135,361)
(136,366)(137,365)(138,364)(139,372)(140,371)(141,370)(142,369)(143,368)
(144,367)(145,291)(146,290)(147,289)(148,294)(149,293)(150,292)(151,300)
(152,299)(153,298)(154,297)(155,296)(156,295)(157,309)(158,308)(159,307)
(160,312)(161,311)(162,310)(163,303)(164,302)(165,301)(166,306)(167,305)
(168,304)(169,327)(170,326)(171,325)(172,330)(173,329)(174,328)(175,336)
(176,335)(177,334)(178,333)(179,332)(180,331)(181,315)(182,314)(183,313)
(184,318)(185,317)(186,316)(187,324)(188,323)(189,322)(190,321)(191,320)
(192,319);
poly := sub<Sym(384)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope