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Polytope of Type {4,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,12}*768f
if this polytope has a name.
Group : SmallGroup(768,1088927)
Rank : 4
Schlafli Type : {4,4,12}
Number of vertices, edges, etc : 4, 16, 48, 24
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
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 : {4,4,6}*384d, {2,4,12}*384c
   4-fold quotients : {4,4,3}*192b, {2,4,6}*192
   8-fold quotients : {4,2,6}*96, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   16-fold quotients : {4,2,3}*48, {2,4,3}*48, {2,2,6}*48
   24-fold quotients : {4,2,2}*32
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,193)(  2,194)(  3,195)(  4,196)(  5,197)(  6,198)(  7,199)(  8,200)
(  9,201)( 10,202)( 11,203)( 12,204)( 13,205)( 14,206)( 15,207)( 16,208)
( 17,209)( 18,210)( 19,211)( 20,212)( 21,213)( 22,214)( 23,215)( 24,216)
( 25,217)( 26,218)( 27,219)( 28,220)( 29,221)( 30,222)( 31,223)( 32,224)
( 33,225)( 34,226)( 35,227)( 36,228)( 37,229)( 38,230)( 39,231)( 40,232)
( 41,233)( 42,234)( 43,235)( 44,236)( 45,237)( 46,238)( 47,239)( 48,240)
( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,259)( 56,260)
( 57,261)( 58,262)( 59,263)( 60,264)( 61,241)( 62,242)( 63,243)( 64,244)
( 65,245)( 66,246)( 67,247)( 68,248)( 69,249)( 70,250)( 71,251)( 72,252)
( 73,277)( 74,278)( 75,279)( 76,280)( 77,281)( 78,282)( 79,283)( 80,284)
( 81,285)( 82,286)( 83,287)( 84,288)( 85,265)( 86,266)( 87,267)( 88,268)
( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)( 96,276)
( 97,301)( 98,302)( 99,303)(100,304)(101,305)(102,306)(103,307)(104,308)
(105,309)(106,310)(107,311)(108,312)(109,289)(110,290)(111,291)(112,292)
(113,293)(114,294)(115,295)(116,296)(117,297)(118,298)(119,299)(120,300)
(121,325)(122,326)(123,327)(124,328)(125,329)(126,330)(127,331)(128,332)
(129,333)(130,334)(131,335)(132,336)(133,313)(134,314)(135,315)(136,316)
(137,317)(138,318)(139,319)(140,320)(141,321)(142,322)(143,323)(144,324)
(145,337)(146,338)(147,339)(148,340)(149,341)(150,342)(151,343)(152,344)
(153,345)(154,346)(155,347)(156,348)(157,349)(158,350)(159,351)(160,352)
(161,353)(162,354)(163,355)(164,356)(165,357)(166,358)(167,359)(168,360)
(169,361)(170,362)(171,363)(172,364)(173,365)(174,366)(175,367)(176,368)
(177,369)(178,370)(179,371)(180,372)(181,373)(182,374)(183,375)(184,376)
(185,377)(186,378)(187,379)(188,380)(189,381)(190,382)(191,383)(192,384);;
s1 := (  1,100)(  2, 99)(  3, 98)(  4, 97)(  5,104)(  6,103)(  7,102)(  8,101)
(  9,108)( 10,107)( 11,106)( 12,105)( 13,112)( 14,111)( 15,110)( 16,109)
( 17,116)( 18,115)( 19,114)( 20,113)( 21,120)( 22,119)( 23,118)( 24,117)
( 25,124)( 26,123)( 27,122)( 28,121)( 29,128)( 30,127)( 31,126)( 32,125)
( 33,132)( 34,131)( 35,130)( 36,129)( 37,136)( 38,135)( 39,134)( 40,133)
( 41,140)( 42,139)( 43,138)( 44,137)( 45,144)( 46,143)( 47,142)( 48,141)
( 49,172)( 50,171)( 51,170)( 52,169)( 53,176)( 54,175)( 55,174)( 56,173)
( 57,180)( 58,179)( 59,178)( 60,177)( 61,184)( 62,183)( 63,182)( 64,181)
( 65,188)( 66,187)( 67,186)( 68,185)( 69,192)( 70,191)( 71,190)( 72,189)
( 73,148)( 74,147)( 75,146)( 76,145)( 77,152)( 78,151)( 79,150)( 80,149)
( 81,156)( 82,155)( 83,154)( 84,153)( 85,160)( 86,159)( 87,158)( 88,157)
( 89,164)( 90,163)( 91,162)( 92,161)( 93,168)( 94,167)( 95,166)( 96,165)
(193,292)(194,291)(195,290)(196,289)(197,296)(198,295)(199,294)(200,293)
(201,300)(202,299)(203,298)(204,297)(205,304)(206,303)(207,302)(208,301)
(209,308)(210,307)(211,306)(212,305)(213,312)(214,311)(215,310)(216,309)
(217,316)(218,315)(219,314)(220,313)(221,320)(222,319)(223,318)(224,317)
(225,324)(226,323)(227,322)(228,321)(229,328)(230,327)(231,326)(232,325)
(233,332)(234,331)(235,330)(236,329)(237,336)(238,335)(239,334)(240,333)
(241,364)(242,363)(243,362)(244,361)(245,368)(246,367)(247,366)(248,365)
(249,372)(250,371)(251,370)(252,369)(253,376)(254,375)(255,374)(256,373)
(257,380)(258,379)(259,378)(260,377)(261,384)(262,383)(263,382)(264,381)
(265,340)(266,339)(267,338)(268,337)(269,344)(270,343)(271,342)(272,341)
(273,348)(274,347)(275,346)(276,345)(277,352)(278,351)(279,350)(280,349)
(281,356)(282,355)(283,354)(284,353)(285,360)(286,359)(287,358)(288,357);;
s2 := (  1, 49)(  2, 50)(  3, 52)(  4, 51)(  5, 57)(  6, 58)(  7, 60)(  8, 59)
(  9, 53)( 10, 54)( 11, 56)( 12, 55)( 13, 61)( 14, 62)( 15, 64)( 16, 63)
( 17, 69)( 18, 70)( 19, 72)( 20, 71)( 21, 65)( 22, 66)( 23, 68)( 24, 67)
( 25, 73)( 26, 74)( 27, 76)( 28, 75)( 29, 81)( 30, 82)( 31, 84)( 32, 83)
( 33, 77)( 34, 78)( 35, 80)( 36, 79)( 37, 85)( 38, 86)( 39, 88)( 40, 87)
( 41, 93)( 42, 94)( 43, 96)( 44, 95)( 45, 89)( 46, 90)( 47, 92)( 48, 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)
(121,169)(122,170)(123,172)(124,171)(125,177)(126,178)(127,180)(128,179)
(129,173)(130,174)(131,176)(132,175)(133,181)(134,182)(135,184)(136,183)
(137,189)(138,190)(139,192)(140,191)(141,185)(142,186)(143,188)(144,187)
(193,253)(194,254)(195,256)(196,255)(197,261)(198,262)(199,264)(200,263)
(201,257)(202,258)(203,260)(204,259)(205,241)(206,242)(207,244)(208,243)
(209,249)(210,250)(211,252)(212,251)(213,245)(214,246)(215,248)(216,247)
(217,277)(218,278)(219,280)(220,279)(221,285)(222,286)(223,288)(224,287)
(225,281)(226,282)(227,284)(228,283)(229,265)(230,266)(231,268)(232,267)
(233,273)(234,274)(235,276)(236,275)(237,269)(238,270)(239,272)(240,271)
(289,349)(290,350)(291,352)(292,351)(293,357)(294,358)(295,360)(296,359)
(297,353)(298,354)(299,356)(300,355)(301,337)(302,338)(303,340)(304,339)
(305,345)(306,346)(307,348)(308,347)(309,341)(310,342)(311,344)(312,343)
(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);;
s3 := (  1,105)(  2,107)(  3,106)(  4,108)(  5,101)(  6,103)(  7,102)(  8,104)
(  9, 97)( 10, 99)( 11, 98)( 12,100)( 13,117)( 14,119)( 15,118)( 16,120)
( 17,113)( 18,115)( 19,114)( 20,116)( 21,109)( 22,111)( 23,110)( 24,112)
( 25,129)( 26,131)( 27,130)( 28,132)( 29,125)( 30,127)( 31,126)( 32,128)
( 33,121)( 34,123)( 35,122)( 36,124)( 37,141)( 38,143)( 39,142)( 40,144)
( 41,137)( 42,139)( 43,138)( 44,140)( 45,133)( 46,135)( 47,134)( 48,136)
( 49,177)( 50,179)( 51,178)( 52,180)( 53,173)( 54,175)( 55,174)( 56,176)
( 57,169)( 58,171)( 59,170)( 60,172)( 61,189)( 62,191)( 63,190)( 64,192)
( 65,185)( 66,187)( 67,186)( 68,188)( 69,181)( 70,183)( 71,182)( 72,184)
( 73,153)( 74,155)( 75,154)( 76,156)( 77,149)( 78,151)( 79,150)( 80,152)
( 81,145)( 82,147)( 83,146)( 84,148)( 85,165)( 86,167)( 87,166)( 88,168)
( 89,161)( 90,163)( 91,162)( 92,164)( 93,157)( 94,159)( 95,158)( 96,160)
(193,309)(194,311)(195,310)(196,312)(197,305)(198,307)(199,306)(200,308)
(201,301)(202,303)(203,302)(204,304)(205,297)(206,299)(207,298)(208,300)
(209,293)(210,295)(211,294)(212,296)(213,289)(214,291)(215,290)(216,292)
(217,333)(218,335)(219,334)(220,336)(221,329)(222,331)(223,330)(224,332)
(225,325)(226,327)(227,326)(228,328)(229,321)(230,323)(231,322)(232,324)
(233,317)(234,319)(235,318)(236,320)(237,313)(238,315)(239,314)(240,316)
(241,381)(242,383)(243,382)(244,384)(245,377)(246,379)(247,378)(248,380)
(249,373)(250,375)(251,374)(252,376)(253,369)(254,371)(255,370)(256,372)
(257,365)(258,367)(259,366)(260,368)(261,361)(262,363)(263,362)(264,364)
(265,357)(266,359)(267,358)(268,360)(269,353)(270,355)(271,354)(272,356)
(273,349)(274,351)(275,350)(276,352)(277,345)(278,347)(279,346)(280,348)
(281,341)(282,343)(283,342)(284,344)(285,337)(286,339)(287,338)(288,340);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(384)!(  1,193)(  2,194)(  3,195)(  4,196)(  5,197)(  6,198)(  7,199)
(  8,200)(  9,201)( 10,202)( 11,203)( 12,204)( 13,205)( 14,206)( 15,207)
( 16,208)( 17,209)( 18,210)( 19,211)( 20,212)( 21,213)( 22,214)( 23,215)
( 24,216)( 25,217)( 26,218)( 27,219)( 28,220)( 29,221)( 30,222)( 31,223)
( 32,224)( 33,225)( 34,226)( 35,227)( 36,228)( 37,229)( 38,230)( 39,231)
( 40,232)( 41,233)( 42,234)( 43,235)( 44,236)( 45,237)( 46,238)( 47,239)
( 48,240)( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,259)
( 56,260)( 57,261)( 58,262)( 59,263)( 60,264)( 61,241)( 62,242)( 63,243)
( 64,244)( 65,245)( 66,246)( 67,247)( 68,248)( 69,249)( 70,250)( 71,251)
( 72,252)( 73,277)( 74,278)( 75,279)( 76,280)( 77,281)( 78,282)( 79,283)
( 80,284)( 81,285)( 82,286)( 83,287)( 84,288)( 85,265)( 86,266)( 87,267)
( 88,268)( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)
( 96,276)( 97,301)( 98,302)( 99,303)(100,304)(101,305)(102,306)(103,307)
(104,308)(105,309)(106,310)(107,311)(108,312)(109,289)(110,290)(111,291)
(112,292)(113,293)(114,294)(115,295)(116,296)(117,297)(118,298)(119,299)
(120,300)(121,325)(122,326)(123,327)(124,328)(125,329)(126,330)(127,331)
(128,332)(129,333)(130,334)(131,335)(132,336)(133,313)(134,314)(135,315)
(136,316)(137,317)(138,318)(139,319)(140,320)(141,321)(142,322)(143,323)
(144,324)(145,337)(146,338)(147,339)(148,340)(149,341)(150,342)(151,343)
(152,344)(153,345)(154,346)(155,347)(156,348)(157,349)(158,350)(159,351)
(160,352)(161,353)(162,354)(163,355)(164,356)(165,357)(166,358)(167,359)
(168,360)(169,361)(170,362)(171,363)(172,364)(173,365)(174,366)(175,367)
(176,368)(177,369)(178,370)(179,371)(180,372)(181,373)(182,374)(183,375)
(184,376)(185,377)(186,378)(187,379)(188,380)(189,381)(190,382)(191,383)
(192,384);
s1 := Sym(384)!(  1,100)(  2, 99)(  3, 98)(  4, 97)(  5,104)(  6,103)(  7,102)
(  8,101)(  9,108)( 10,107)( 11,106)( 12,105)( 13,112)( 14,111)( 15,110)
( 16,109)( 17,116)( 18,115)( 19,114)( 20,113)( 21,120)( 22,119)( 23,118)
( 24,117)( 25,124)( 26,123)( 27,122)( 28,121)( 29,128)( 30,127)( 31,126)
( 32,125)( 33,132)( 34,131)( 35,130)( 36,129)( 37,136)( 38,135)( 39,134)
( 40,133)( 41,140)( 42,139)( 43,138)( 44,137)( 45,144)( 46,143)( 47,142)
( 48,141)( 49,172)( 50,171)( 51,170)( 52,169)( 53,176)( 54,175)( 55,174)
( 56,173)( 57,180)( 58,179)( 59,178)( 60,177)( 61,184)( 62,183)( 63,182)
( 64,181)( 65,188)( 66,187)( 67,186)( 68,185)( 69,192)( 70,191)( 71,190)
( 72,189)( 73,148)( 74,147)( 75,146)( 76,145)( 77,152)( 78,151)( 79,150)
( 80,149)( 81,156)( 82,155)( 83,154)( 84,153)( 85,160)( 86,159)( 87,158)
( 88,157)( 89,164)( 90,163)( 91,162)( 92,161)( 93,168)( 94,167)( 95,166)
( 96,165)(193,292)(194,291)(195,290)(196,289)(197,296)(198,295)(199,294)
(200,293)(201,300)(202,299)(203,298)(204,297)(205,304)(206,303)(207,302)
(208,301)(209,308)(210,307)(211,306)(212,305)(213,312)(214,311)(215,310)
(216,309)(217,316)(218,315)(219,314)(220,313)(221,320)(222,319)(223,318)
(224,317)(225,324)(226,323)(227,322)(228,321)(229,328)(230,327)(231,326)
(232,325)(233,332)(234,331)(235,330)(236,329)(237,336)(238,335)(239,334)
(240,333)(241,364)(242,363)(243,362)(244,361)(245,368)(246,367)(247,366)
(248,365)(249,372)(250,371)(251,370)(252,369)(253,376)(254,375)(255,374)
(256,373)(257,380)(258,379)(259,378)(260,377)(261,384)(262,383)(263,382)
(264,381)(265,340)(266,339)(267,338)(268,337)(269,344)(270,343)(271,342)
(272,341)(273,348)(274,347)(275,346)(276,345)(277,352)(278,351)(279,350)
(280,349)(281,356)(282,355)(283,354)(284,353)(285,360)(286,359)(287,358)
(288,357);
s2 := Sym(384)!(  1, 49)(  2, 50)(  3, 52)(  4, 51)(  5, 57)(  6, 58)(  7, 60)
(  8, 59)(  9, 53)( 10, 54)( 11, 56)( 12, 55)( 13, 61)( 14, 62)( 15, 64)
( 16, 63)( 17, 69)( 18, 70)( 19, 72)( 20, 71)( 21, 65)( 22, 66)( 23, 68)
( 24, 67)( 25, 73)( 26, 74)( 27, 76)( 28, 75)( 29, 81)( 30, 82)( 31, 84)
( 32, 83)( 33, 77)( 34, 78)( 35, 80)( 36, 79)( 37, 85)( 38, 86)( 39, 88)
( 40, 87)( 41, 93)( 42, 94)( 43, 96)( 44, 95)( 45, 89)( 46, 90)( 47, 92)
( 48, 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)(121,169)(122,170)(123,172)(124,171)(125,177)(126,178)(127,180)
(128,179)(129,173)(130,174)(131,176)(132,175)(133,181)(134,182)(135,184)
(136,183)(137,189)(138,190)(139,192)(140,191)(141,185)(142,186)(143,188)
(144,187)(193,253)(194,254)(195,256)(196,255)(197,261)(198,262)(199,264)
(200,263)(201,257)(202,258)(203,260)(204,259)(205,241)(206,242)(207,244)
(208,243)(209,249)(210,250)(211,252)(212,251)(213,245)(214,246)(215,248)
(216,247)(217,277)(218,278)(219,280)(220,279)(221,285)(222,286)(223,288)
(224,287)(225,281)(226,282)(227,284)(228,283)(229,265)(230,266)(231,268)
(232,267)(233,273)(234,274)(235,276)(236,275)(237,269)(238,270)(239,272)
(240,271)(289,349)(290,350)(291,352)(292,351)(293,357)(294,358)(295,360)
(296,359)(297,353)(298,354)(299,356)(300,355)(301,337)(302,338)(303,340)
(304,339)(305,345)(306,346)(307,348)(308,347)(309,341)(310,342)(311,344)
(312,343)(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);
s3 := Sym(384)!(  1,105)(  2,107)(  3,106)(  4,108)(  5,101)(  6,103)(  7,102)
(  8,104)(  9, 97)( 10, 99)( 11, 98)( 12,100)( 13,117)( 14,119)( 15,118)
( 16,120)( 17,113)( 18,115)( 19,114)( 20,116)( 21,109)( 22,111)( 23,110)
( 24,112)( 25,129)( 26,131)( 27,130)( 28,132)( 29,125)( 30,127)( 31,126)
( 32,128)( 33,121)( 34,123)( 35,122)( 36,124)( 37,141)( 38,143)( 39,142)
( 40,144)( 41,137)( 42,139)( 43,138)( 44,140)( 45,133)( 46,135)( 47,134)
( 48,136)( 49,177)( 50,179)( 51,178)( 52,180)( 53,173)( 54,175)( 55,174)
( 56,176)( 57,169)( 58,171)( 59,170)( 60,172)( 61,189)( 62,191)( 63,190)
( 64,192)( 65,185)( 66,187)( 67,186)( 68,188)( 69,181)( 70,183)( 71,182)
( 72,184)( 73,153)( 74,155)( 75,154)( 76,156)( 77,149)( 78,151)( 79,150)
( 80,152)( 81,145)( 82,147)( 83,146)( 84,148)( 85,165)( 86,167)( 87,166)
( 88,168)( 89,161)( 90,163)( 91,162)( 92,164)( 93,157)( 94,159)( 95,158)
( 96,160)(193,309)(194,311)(195,310)(196,312)(197,305)(198,307)(199,306)
(200,308)(201,301)(202,303)(203,302)(204,304)(205,297)(206,299)(207,298)
(208,300)(209,293)(210,295)(211,294)(212,296)(213,289)(214,291)(215,290)
(216,292)(217,333)(218,335)(219,334)(220,336)(221,329)(222,331)(223,330)
(224,332)(225,325)(226,327)(227,326)(228,328)(229,321)(230,323)(231,322)
(232,324)(233,317)(234,319)(235,318)(236,320)(237,313)(238,315)(239,314)
(240,316)(241,381)(242,383)(243,382)(244,384)(245,377)(246,379)(247,378)
(248,380)(249,373)(250,375)(251,374)(252,376)(253,369)(254,371)(255,370)
(256,372)(257,365)(258,367)(259,366)(260,368)(261,361)(262,363)(263,362)
(264,364)(265,357)(266,359)(267,358)(268,360)(269,353)(270,355)(271,354)
(272,356)(273,349)(274,351)(275,350)(276,352)(277,345)(278,347)(279,346)
(280,348)(281,341)(282,343)(283,342)(284,344)(285,337)(286,339)(287,338)
(288,340);
poly := sub<Sym(384)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >; 
 
References : None.
to this polytope