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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}*768a
if this polytope has a name.
Group : SmallGroup(768,81667)
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 : {24,4}*384a, {48,4}*384a, {48,4}*384b
   3-fold quotients : {16,4}*256a
   4-fold quotients : {24,4}*192a, {12,4}*192a, {24,4}*192b, {48,2}*192
   6-fold quotients : {8,4}*128a, {16,4}*128a, {16,4}*128b
   8-fold quotients : {12,4}*96a, {24,2}*96
   12-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64, {16,2}*64
   16-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {4,4}*32, {8,2}*32
   32-fold quotients : {6,2}*24
   48-fold quotients : {2,4}*16, {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 := (  1,193)(  2,195)(  3,194)(  4,196)(  5,198)(  6,197)(  7,199)(  8,201)
(  9,200)( 10,202)( 11,204)( 12,203)( 13,208)( 14,210)( 15,209)( 16,205)
( 17,207)( 18,206)( 19,214)( 20,216)( 21,215)( 22,211)( 23,213)( 24,212)
( 25,223)( 26,225)( 27,224)( 28,226)( 29,228)( 30,227)( 31,217)( 32,219)
( 33,218)( 34,220)( 35,222)( 36,221)( 37,238)( 38,240)( 39,239)( 40,235)
( 41,237)( 42,236)( 43,232)( 44,234)( 45,233)( 46,229)( 47,231)( 48,230)
( 49,253)( 50,255)( 51,254)( 52,256)( 53,258)( 54,257)( 55,259)( 56,261)
( 57,260)( 58,262)( 59,264)( 60,263)( 61,241)( 62,243)( 63,242)( 64,244)
( 65,246)( 66,245)( 67,247)( 68,249)( 69,248)( 70,250)( 71,252)( 72,251)
( 73,283)( 74,285)( 75,284)( 76,286)( 77,288)( 78,287)( 79,277)( 80,279)
( 81,278)( 82,280)( 83,282)( 84,281)( 85,271)( 86,273)( 87,272)( 88,274)
( 89,276)( 90,275)( 91,265)( 92,267)( 93,266)( 94,268)( 95,270)( 96,269)
( 97,289)( 98,291)( 99,290)(100,292)(101,294)(102,293)(103,295)(104,297)
(105,296)(106,298)(107,300)(108,299)(109,304)(110,306)(111,305)(112,301)
(113,303)(114,302)(115,310)(116,312)(117,311)(118,307)(119,309)(120,308)
(121,319)(122,321)(123,320)(124,322)(125,324)(126,323)(127,313)(128,315)
(129,314)(130,316)(131,318)(132,317)(133,334)(134,336)(135,335)(136,331)
(137,333)(138,332)(139,328)(140,330)(141,329)(142,325)(143,327)(144,326)
(145,349)(146,351)(147,350)(148,352)(149,354)(150,353)(151,355)(152,357)
(153,356)(154,358)(155,360)(156,359)(157,337)(158,339)(159,338)(160,340)
(161,342)(162,341)(163,343)(164,345)(165,344)(166,346)(167,348)(168,347)
(169,379)(170,381)(171,380)(172,382)(173,384)(174,383)(175,373)(176,375)
(177,374)(178,376)(179,378)(180,377)(181,367)(182,369)(183,368)(184,370)
(185,372)(186,371)(187,361)(188,363)(189,362)(190,364)(191,366)(192,365);;
s1 := (  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)( 19, 24)
( 20, 23)( 21, 22)( 25, 27)( 28, 30)( 31, 33)( 34, 36)( 37, 42)( 38, 41)
( 39, 40)( 43, 48)( 44, 47)( 45, 46)( 49, 63)( 50, 62)( 51, 61)( 52, 66)
( 53, 65)( 54, 64)( 55, 69)( 56, 68)( 57, 67)( 58, 72)( 59, 71)( 60, 70)
( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)( 79, 93)( 80, 92)
( 81, 91)( 82, 96)( 83, 95)( 84, 94)( 97,123)( 98,122)( 99,121)(100,126)
(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)(108,130)
(109,138)(110,137)(111,136)(112,135)(113,134)(114,133)(115,144)(116,143)
(117,142)(118,141)(119,140)(120,139)(145,183)(146,182)(147,181)(148,186)
(149,185)(150,184)(151,189)(152,188)(153,187)(154,192)(155,191)(156,190)
(157,171)(158,170)(159,169)(160,174)(161,173)(162,172)(163,177)(164,176)
(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)(195,241)(196,246)
(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)(204,250)
(205,258)(206,257)(207,256)(208,255)(209,254)(210,253)(211,264)(212,263)
(213,262)(214,261)(215,260)(216,259)(217,267)(218,266)(219,265)(220,270)
(221,269)(222,268)(223,273)(224,272)(225,271)(226,276)(227,275)(228,274)
(229,282)(230,281)(231,280)(232,279)(233,278)(234,277)(235,288)(236,287)
(237,286)(238,285)(239,284)(240,283)(289,369)(290,368)(291,367)(292,372)
(293,371)(294,370)(295,363)(296,362)(297,361)(298,366)(299,365)(300,364)
(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)(307,378)(308,377)
(309,376)(310,375)(311,374)(312,373)(313,345)(314,344)(315,343)(316,348)
(317,347)(318,346)(319,339)(320,338)(321,337)(322,342)(323,341)(324,340)
(325,360)(326,359)(327,358)(328,357)(329,356)(330,355)(331,354)(332,353)
(333,352)(334,351)(335,350)(336,349);;
s2 := (  1, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,103)(  8,104)
(  9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)( 16,112)
( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)( 24,120)
( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)
( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)( 48,144)
( 49,151)( 50,152)( 51,153)( 52,154)( 53,155)( 54,156)( 55,145)( 56,146)
( 57,147)( 58,148)( 59,149)( 60,150)( 61,163)( 62,164)( 63,165)( 64,166)
( 65,167)( 66,168)( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)( 72,162)
( 73,175)( 74,176)( 75,177)( 76,178)( 77,179)( 78,180)( 79,169)( 80,170)
( 81,171)( 82,172)( 83,173)( 84,174)( 85,187)( 86,188)( 87,189)( 88,190)
( 89,191)( 90,192)( 91,181)( 92,182)( 93,183)( 94,184)( 95,185)( 96,186)
(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)(200,296)
(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)(208,304)
(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)(216,312)
(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)(224,320)
(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)(232,328)
(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)(240,336)
(241,343)(242,344)(243,345)(244,346)(245,347)(246,348)(247,337)(248,338)
(249,339)(250,340)(251,341)(252,342)(253,355)(254,356)(255,357)(256,358)
(257,359)(258,360)(259,349)(260,350)(261,351)(262,352)(263,353)(264,354)
(265,367)(266,368)(267,369)(268,370)(269,371)(270,372)(271,361)(272,362)
(273,363)(274,364)(275,365)(276,366)(277,379)(278,380)(279,381)(280,382)
(281,383)(282,384)(283,373)(284,374)(285,375)(286,376)(287,377)(288,378);;
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*s2*s1*s2*s1*s0*s1*s0*s2*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)!(  1,193)(  2,195)(  3,194)(  4,196)(  5,198)(  6,197)(  7,199)
(  8,201)(  9,200)( 10,202)( 11,204)( 12,203)( 13,208)( 14,210)( 15,209)
( 16,205)( 17,207)( 18,206)( 19,214)( 20,216)( 21,215)( 22,211)( 23,213)
( 24,212)( 25,223)( 26,225)( 27,224)( 28,226)( 29,228)( 30,227)( 31,217)
( 32,219)( 33,218)( 34,220)( 35,222)( 36,221)( 37,238)( 38,240)( 39,239)
( 40,235)( 41,237)( 42,236)( 43,232)( 44,234)( 45,233)( 46,229)( 47,231)
( 48,230)( 49,253)( 50,255)( 51,254)( 52,256)( 53,258)( 54,257)( 55,259)
( 56,261)( 57,260)( 58,262)( 59,264)( 60,263)( 61,241)( 62,243)( 63,242)
( 64,244)( 65,246)( 66,245)( 67,247)( 68,249)( 69,248)( 70,250)( 71,252)
( 72,251)( 73,283)( 74,285)( 75,284)( 76,286)( 77,288)( 78,287)( 79,277)
( 80,279)( 81,278)( 82,280)( 83,282)( 84,281)( 85,271)( 86,273)( 87,272)
( 88,274)( 89,276)( 90,275)( 91,265)( 92,267)( 93,266)( 94,268)( 95,270)
( 96,269)( 97,289)( 98,291)( 99,290)(100,292)(101,294)(102,293)(103,295)
(104,297)(105,296)(106,298)(107,300)(108,299)(109,304)(110,306)(111,305)
(112,301)(113,303)(114,302)(115,310)(116,312)(117,311)(118,307)(119,309)
(120,308)(121,319)(122,321)(123,320)(124,322)(125,324)(126,323)(127,313)
(128,315)(129,314)(130,316)(131,318)(132,317)(133,334)(134,336)(135,335)
(136,331)(137,333)(138,332)(139,328)(140,330)(141,329)(142,325)(143,327)
(144,326)(145,349)(146,351)(147,350)(148,352)(149,354)(150,353)(151,355)
(152,357)(153,356)(154,358)(155,360)(156,359)(157,337)(158,339)(159,338)
(160,340)(161,342)(162,341)(163,343)(164,345)(165,344)(166,346)(167,348)
(168,347)(169,379)(170,381)(171,380)(172,382)(173,384)(174,383)(175,373)
(176,375)(177,374)(178,376)(179,378)(180,377)(181,367)(182,369)(183,368)
(184,370)(185,372)(186,371)(187,361)(188,363)(189,362)(190,364)(191,366)
(192,365);
s1 := Sym(384)!(  1,  3)(  4,  6)(  7,  9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)
( 19, 24)( 20, 23)( 21, 22)( 25, 27)( 28, 30)( 31, 33)( 34, 36)( 37, 42)
( 38, 41)( 39, 40)( 43, 48)( 44, 47)( 45, 46)( 49, 63)( 50, 62)( 51, 61)
( 52, 66)( 53, 65)( 54, 64)( 55, 69)( 56, 68)( 57, 67)( 58, 72)( 59, 71)
( 60, 70)( 73, 87)( 74, 86)( 75, 85)( 76, 90)( 77, 89)( 78, 88)( 79, 93)
( 80, 92)( 81, 91)( 82, 96)( 83, 95)( 84, 94)( 97,123)( 98,122)( 99,121)
(100,126)(101,125)(102,124)(103,129)(104,128)(105,127)(106,132)(107,131)
(108,130)(109,138)(110,137)(111,136)(112,135)(113,134)(114,133)(115,144)
(116,143)(117,142)(118,141)(119,140)(120,139)(145,183)(146,182)(147,181)
(148,186)(149,185)(150,184)(151,189)(152,188)(153,187)(154,192)(155,191)
(156,190)(157,171)(158,170)(159,169)(160,174)(161,173)(162,172)(163,177)
(164,176)(165,175)(166,180)(167,179)(168,178)(193,243)(194,242)(195,241)
(196,246)(197,245)(198,244)(199,249)(200,248)(201,247)(202,252)(203,251)
(204,250)(205,258)(206,257)(207,256)(208,255)(209,254)(210,253)(211,264)
(212,263)(213,262)(214,261)(215,260)(216,259)(217,267)(218,266)(219,265)
(220,270)(221,269)(222,268)(223,273)(224,272)(225,271)(226,276)(227,275)
(228,274)(229,282)(230,281)(231,280)(232,279)(233,278)(234,277)(235,288)
(236,287)(237,286)(238,285)(239,284)(240,283)(289,369)(290,368)(291,367)
(292,372)(293,371)(294,370)(295,363)(296,362)(297,361)(298,366)(299,365)
(300,364)(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)(307,378)
(308,377)(309,376)(310,375)(311,374)(312,373)(313,345)(314,344)(315,343)
(316,348)(317,347)(318,346)(319,339)(320,338)(321,337)(322,342)(323,341)
(324,340)(325,360)(326,359)(327,358)(328,357)(329,356)(330,355)(331,354)
(332,353)(333,352)(334,351)(335,350)(336,349);
s2 := Sym(384)!(  1, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,103)
(  8,104)(  9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)
( 16,112)( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)
( 24,120)( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)
( 32,128)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)
( 40,136)( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)
( 48,144)( 49,151)( 50,152)( 51,153)( 52,154)( 53,155)( 54,156)( 55,145)
( 56,146)( 57,147)( 58,148)( 59,149)( 60,150)( 61,163)( 62,164)( 63,165)
( 64,166)( 65,167)( 66,168)( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)
( 72,162)( 73,175)( 74,176)( 75,177)( 76,178)( 77,179)( 78,180)( 79,169)
( 80,170)( 81,171)( 82,172)( 83,173)( 84,174)( 85,187)( 86,188)( 87,189)
( 88,190)( 89,191)( 90,192)( 91,181)( 92,182)( 93,183)( 94,184)( 95,185)
( 96,186)(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)
(200,296)(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)
(208,304)(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)
(216,312)(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)
(224,320)(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)
(232,328)(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)
(240,336)(241,343)(242,344)(243,345)(244,346)(245,347)(246,348)(247,337)
(248,338)(249,339)(250,340)(251,341)(252,342)(253,355)(254,356)(255,357)
(256,358)(257,359)(258,360)(259,349)(260,350)(261,351)(262,352)(263,353)
(264,354)(265,367)(266,368)(267,369)(268,370)(269,371)(270,372)(271,361)
(272,362)(273,363)(274,364)(275,365)(276,366)(277,379)(278,380)(279,381)
(280,382)(281,383)(282,384)(283,373)(284,374)(285,375)(286,376)(287,377)
(288,378);
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*s2*s1*s2*s1*s0*s1*s0*s2*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