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Polytope of Type {48,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,4}*768c
if this polytope has a name.
Group : SmallGroup(768,1088569)
Rank : 3
Schlafli Type : {48,4}
Number of vertices, edges, etc : 96, 192, 8
Order of s0s1s2 : 48
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {48,4}*384c, {48,4}*384d, {24,4}*384c
   4-fold quotients : {48,2}*192, {24,4}*192c, {24,4}*192d, {12,4}*192b
   8-fold quotients : {24,2}*96, {12,4}*96b, {12,4}*96c, {6,4}*96
   12-fold quotients : {16,2}*64
   16-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   24-fold quotients : {8,2}*32
   32-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {4,2}*16
   64-fold quotients : {3,2}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 15, 16)( 17, 21)( 18, 22)
( 19, 24)( 20, 23)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)( 30, 46)
( 31, 48)( 32, 47)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 49, 73)( 50, 74)
( 51, 76)( 52, 75)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 57, 77)( 58, 78)
( 59, 80)( 60, 79)( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 65, 93)( 66, 94)
( 67, 96)( 68, 95)( 69, 89)( 70, 90)( 71, 92)( 72, 91)( 97,145)( 98,146)
( 99,148)(100,147)(101,153)(102,154)(103,156)(104,155)(105,149)(106,150)
(107,152)(108,151)(109,157)(110,158)(111,160)(112,159)(113,165)(114,166)
(115,168)(116,167)(117,161)(118,162)(119,164)(120,163)(121,181)(122,182)
(123,184)(124,183)(125,189)(126,190)(127,192)(128,191)(129,185)(130,186)
(131,188)(132,187)(133,169)(134,170)(135,172)(136,171)(137,177)(138,178)
(139,180)(140,179)(141,173)(142,174)(143,176)(144,175)(195,196)(197,201)
(198,202)(199,204)(200,203)(207,208)(209,213)(210,214)(211,216)(212,215)
(217,229)(218,230)(219,232)(220,231)(221,237)(222,238)(223,240)(224,239)
(225,233)(226,234)(227,236)(228,235)(241,265)(242,266)(243,268)(244,267)
(245,273)(246,274)(247,276)(248,275)(249,269)(250,270)(251,272)(252,271)
(253,277)(254,278)(255,280)(256,279)(257,285)(258,286)(259,288)(260,287)
(261,281)(262,282)(263,284)(264,283)(289,337)(290,338)(291,340)(292,339)
(293,345)(294,346)(295,348)(296,347)(297,341)(298,342)(299,344)(300,343)
(301,349)(302,350)(303,352)(304,351)(305,357)(306,358)(307,360)(308,359)
(309,353)(310,354)(311,356)(312,355)(313,373)(314,374)(315,376)(316,375)
(317,381)(318,382)(319,384)(320,383)(321,377)(322,378)(323,380)(324,379)
(325,361)(326,362)(327,364)(328,363)(329,369)(330,370)(331,372)(332,371)
(333,365)(334,366)(335,368)(336,367);;
s1 := (  1,153)(  2,155)(  3,154)(  4,156)(  5,149)(  6,151)(  7,150)(  8,152)
(  9,145)( 10,147)( 11,146)( 12,148)( 13,165)( 14,167)( 15,166)( 16,168)
( 17,161)( 18,163)( 19,162)( 20,164)( 21,157)( 22,159)( 23,158)( 24,160)
( 25,189)( 26,191)( 27,190)( 28,192)( 29,185)( 30,187)( 31,186)( 32,188)
( 33,181)( 34,183)( 35,182)( 36,184)( 37,177)( 38,179)( 39,178)( 40,180)
( 41,173)( 42,175)( 43,174)( 44,176)( 45,169)( 46,171)( 47,170)( 48,172)
( 49,105)( 50,107)( 51,106)( 52,108)( 53,101)( 54,103)( 55,102)( 56,104)
( 57, 97)( 58, 99)( 59, 98)( 60,100)( 61,117)( 62,119)( 63,118)( 64,120)
( 65,113)( 66,115)( 67,114)( 68,116)( 69,109)( 70,111)( 71,110)( 72,112)
( 73,141)( 74,143)( 75,142)( 76,144)( 77,137)( 78,139)( 79,138)( 80,140)
( 81,133)( 82,135)( 83,134)( 84,136)( 85,129)( 86,131)( 87,130)( 88,132)
( 89,125)( 90,127)( 91,126)( 92,128)( 93,121)( 94,123)( 95,122)( 96,124)
(193,345)(194,347)(195,346)(196,348)(197,341)(198,343)(199,342)(200,344)
(201,337)(202,339)(203,338)(204,340)(205,357)(206,359)(207,358)(208,360)
(209,353)(210,355)(211,354)(212,356)(213,349)(214,351)(215,350)(216,352)
(217,381)(218,383)(219,382)(220,384)(221,377)(222,379)(223,378)(224,380)
(225,373)(226,375)(227,374)(228,376)(229,369)(230,371)(231,370)(232,372)
(233,365)(234,367)(235,366)(236,368)(237,361)(238,363)(239,362)(240,364)
(241,297)(242,299)(243,298)(244,300)(245,293)(246,295)(247,294)(248,296)
(249,289)(250,291)(251,290)(252,292)(253,309)(254,311)(255,310)(256,312)
(257,305)(258,307)(259,306)(260,308)(261,301)(262,303)(263,302)(264,304)
(265,333)(266,335)(267,334)(268,336)(269,329)(270,331)(271,330)(272,332)
(273,325)(274,327)(275,326)(276,328)(277,321)(278,323)(279,322)(280,324)
(281,317)(282,319)(283,318)(284,320)(285,313)(286,315)(287,314)(288,316);;
s2 := (  1,194)(  2,193)(  3,196)(  4,195)(  5,198)(  6,197)(  7,200)(  8,199)
(  9,202)( 10,201)( 11,204)( 12,203)( 13,206)( 14,205)( 15,208)( 16,207)
( 17,210)( 18,209)( 19,212)( 20,211)( 21,214)( 22,213)( 23,216)( 24,215)
( 25,218)( 26,217)( 27,220)( 28,219)( 29,222)( 30,221)( 31,224)( 32,223)
( 33,226)( 34,225)( 35,228)( 36,227)( 37,230)( 38,229)( 39,232)( 40,231)
( 41,234)( 42,233)( 43,236)( 44,235)( 45,238)( 46,237)( 47,240)( 48,239)
( 49,242)( 50,241)( 51,244)( 52,243)( 53,246)( 54,245)( 55,248)( 56,247)
( 57,250)( 58,249)( 59,252)( 60,251)( 61,254)( 62,253)( 63,256)( 64,255)
( 65,258)( 66,257)( 67,260)( 68,259)( 69,262)( 70,261)( 71,264)( 72,263)
( 73,266)( 74,265)( 75,268)( 76,267)( 77,270)( 78,269)( 79,272)( 80,271)
( 81,274)( 82,273)( 83,276)( 84,275)( 85,278)( 86,277)( 87,280)( 88,279)
( 89,282)( 90,281)( 91,284)( 92,283)( 93,286)( 94,285)( 95,288)( 96,287)
( 97,290)( 98,289)( 99,292)(100,291)(101,294)(102,293)(103,296)(104,295)
(105,298)(106,297)(107,300)(108,299)(109,302)(110,301)(111,304)(112,303)
(113,306)(114,305)(115,308)(116,307)(117,310)(118,309)(119,312)(120,311)
(121,314)(122,313)(123,316)(124,315)(125,318)(126,317)(127,320)(128,319)
(129,322)(130,321)(131,324)(132,323)(133,326)(134,325)(135,328)(136,327)
(137,330)(138,329)(139,332)(140,331)(141,334)(142,333)(143,336)(144,335)
(145,338)(146,337)(147,340)(148,339)(149,342)(150,341)(151,344)(152,343)
(153,346)(154,345)(155,348)(156,347)(157,350)(158,349)(159,352)(160,351)
(161,354)(162,353)(163,356)(164,355)(165,358)(166,357)(167,360)(168,359)
(169,362)(170,361)(171,364)(172,363)(173,366)(174,365)(175,368)(176,367)
(177,370)(178,369)(179,372)(180,371)(181,374)(182,373)(183,376)(184,375)
(185,378)(186,377)(187,380)(188,379)(189,382)(190,381)(191,384)(192,383);;
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, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 15, 16)( 17, 21)
( 18, 22)( 19, 24)( 20, 23)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)
( 30, 46)( 31, 48)( 32, 47)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 49, 73)
( 50, 74)( 51, 76)( 52, 75)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 57, 77)
( 58, 78)( 59, 80)( 60, 79)( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 65, 93)
( 66, 94)( 67, 96)( 68, 95)( 69, 89)( 70, 90)( 71, 92)( 72, 91)( 97,145)
( 98,146)( 99,148)(100,147)(101,153)(102,154)(103,156)(104,155)(105,149)
(106,150)(107,152)(108,151)(109,157)(110,158)(111,160)(112,159)(113,165)
(114,166)(115,168)(116,167)(117,161)(118,162)(119,164)(120,163)(121,181)
(122,182)(123,184)(124,183)(125,189)(126,190)(127,192)(128,191)(129,185)
(130,186)(131,188)(132,187)(133,169)(134,170)(135,172)(136,171)(137,177)
(138,178)(139,180)(140,179)(141,173)(142,174)(143,176)(144,175)(195,196)
(197,201)(198,202)(199,204)(200,203)(207,208)(209,213)(210,214)(211,216)
(212,215)(217,229)(218,230)(219,232)(220,231)(221,237)(222,238)(223,240)
(224,239)(225,233)(226,234)(227,236)(228,235)(241,265)(242,266)(243,268)
(244,267)(245,273)(246,274)(247,276)(248,275)(249,269)(250,270)(251,272)
(252,271)(253,277)(254,278)(255,280)(256,279)(257,285)(258,286)(259,288)
(260,287)(261,281)(262,282)(263,284)(264,283)(289,337)(290,338)(291,340)
(292,339)(293,345)(294,346)(295,348)(296,347)(297,341)(298,342)(299,344)
(300,343)(301,349)(302,350)(303,352)(304,351)(305,357)(306,358)(307,360)
(308,359)(309,353)(310,354)(311,356)(312,355)(313,373)(314,374)(315,376)
(316,375)(317,381)(318,382)(319,384)(320,383)(321,377)(322,378)(323,380)
(324,379)(325,361)(326,362)(327,364)(328,363)(329,369)(330,370)(331,372)
(332,371)(333,365)(334,366)(335,368)(336,367);
s1 := Sym(384)!(  1,153)(  2,155)(  3,154)(  4,156)(  5,149)(  6,151)(  7,150)
(  8,152)(  9,145)( 10,147)( 11,146)( 12,148)( 13,165)( 14,167)( 15,166)
( 16,168)( 17,161)( 18,163)( 19,162)( 20,164)( 21,157)( 22,159)( 23,158)
( 24,160)( 25,189)( 26,191)( 27,190)( 28,192)( 29,185)( 30,187)( 31,186)
( 32,188)( 33,181)( 34,183)( 35,182)( 36,184)( 37,177)( 38,179)( 39,178)
( 40,180)( 41,173)( 42,175)( 43,174)( 44,176)( 45,169)( 46,171)( 47,170)
( 48,172)( 49,105)( 50,107)( 51,106)( 52,108)( 53,101)( 54,103)( 55,102)
( 56,104)( 57, 97)( 58, 99)( 59, 98)( 60,100)( 61,117)( 62,119)( 63,118)
( 64,120)( 65,113)( 66,115)( 67,114)( 68,116)( 69,109)( 70,111)( 71,110)
( 72,112)( 73,141)( 74,143)( 75,142)( 76,144)( 77,137)( 78,139)( 79,138)
( 80,140)( 81,133)( 82,135)( 83,134)( 84,136)( 85,129)( 86,131)( 87,130)
( 88,132)( 89,125)( 90,127)( 91,126)( 92,128)( 93,121)( 94,123)( 95,122)
( 96,124)(193,345)(194,347)(195,346)(196,348)(197,341)(198,343)(199,342)
(200,344)(201,337)(202,339)(203,338)(204,340)(205,357)(206,359)(207,358)
(208,360)(209,353)(210,355)(211,354)(212,356)(213,349)(214,351)(215,350)
(216,352)(217,381)(218,383)(219,382)(220,384)(221,377)(222,379)(223,378)
(224,380)(225,373)(226,375)(227,374)(228,376)(229,369)(230,371)(231,370)
(232,372)(233,365)(234,367)(235,366)(236,368)(237,361)(238,363)(239,362)
(240,364)(241,297)(242,299)(243,298)(244,300)(245,293)(246,295)(247,294)
(248,296)(249,289)(250,291)(251,290)(252,292)(253,309)(254,311)(255,310)
(256,312)(257,305)(258,307)(259,306)(260,308)(261,301)(262,303)(263,302)
(264,304)(265,333)(266,335)(267,334)(268,336)(269,329)(270,331)(271,330)
(272,332)(273,325)(274,327)(275,326)(276,328)(277,321)(278,323)(279,322)
(280,324)(281,317)(282,319)(283,318)(284,320)(285,313)(286,315)(287,314)
(288,316);
s2 := Sym(384)!(  1,194)(  2,193)(  3,196)(  4,195)(  5,198)(  6,197)(  7,200)
(  8,199)(  9,202)( 10,201)( 11,204)( 12,203)( 13,206)( 14,205)( 15,208)
( 16,207)( 17,210)( 18,209)( 19,212)( 20,211)( 21,214)( 22,213)( 23,216)
( 24,215)( 25,218)( 26,217)( 27,220)( 28,219)( 29,222)( 30,221)( 31,224)
( 32,223)( 33,226)( 34,225)( 35,228)( 36,227)( 37,230)( 38,229)( 39,232)
( 40,231)( 41,234)( 42,233)( 43,236)( 44,235)( 45,238)( 46,237)( 47,240)
( 48,239)( 49,242)( 50,241)( 51,244)( 52,243)( 53,246)( 54,245)( 55,248)
( 56,247)( 57,250)( 58,249)( 59,252)( 60,251)( 61,254)( 62,253)( 63,256)
( 64,255)( 65,258)( 66,257)( 67,260)( 68,259)( 69,262)( 70,261)( 71,264)
( 72,263)( 73,266)( 74,265)( 75,268)( 76,267)( 77,270)( 78,269)( 79,272)
( 80,271)( 81,274)( 82,273)( 83,276)( 84,275)( 85,278)( 86,277)( 87,280)
( 88,279)( 89,282)( 90,281)( 91,284)( 92,283)( 93,286)( 94,285)( 95,288)
( 96,287)( 97,290)( 98,289)( 99,292)(100,291)(101,294)(102,293)(103,296)
(104,295)(105,298)(106,297)(107,300)(108,299)(109,302)(110,301)(111,304)
(112,303)(113,306)(114,305)(115,308)(116,307)(117,310)(118,309)(119,312)
(120,311)(121,314)(122,313)(123,316)(124,315)(125,318)(126,317)(127,320)
(128,319)(129,322)(130,321)(131,324)(132,323)(133,326)(134,325)(135,328)
(136,327)(137,330)(138,329)(139,332)(140,331)(141,334)(142,333)(143,336)
(144,335)(145,338)(146,337)(147,340)(148,339)(149,342)(150,341)(151,344)
(152,343)(153,346)(154,345)(155,348)(156,347)(157,350)(158,349)(159,352)
(160,351)(161,354)(162,353)(163,356)(164,355)(165,358)(166,357)(167,360)
(168,359)(169,362)(170,361)(171,364)(172,363)(173,366)(174,365)(175,368)
(176,367)(177,370)(178,369)(179,372)(180,371)(181,374)(182,373)(183,376)
(184,375)(185,378)(186,377)(187,380)(188,379)(189,382)(190,381)(191,384)
(192,383);
poly := sub<Sym(384)|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, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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