Polytope of Type {4,3,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,12}*768b
if this polytope has a name.
Group : SmallGroup(768,1088556)
Rank : 4
Schlafli Type : {4,3,12}
Number of vertices, edges, etc : 8, 16, 48, 16
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 4
Special Properties :
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 : {4,3,6}*384b
4-fold quotients : {4,3,3}*192
8-fold quotients : {2,3,6}*96
16-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)
( 9,108)( 10,107)( 11,106)( 12,105)( 13,112)( 14,111)( 15,110)( 16,109)
( 17,118)( 18,117)( 19,120)( 20,119)( 21,114)( 22,113)( 23,116)( 24,115)
( 25,128)( 26,127)( 27,126)( 28,125)( 29,124)( 30,123)( 31,122)( 32,121)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)
( 41,140)( 42,139)( 43,138)( 44,137)( 45,144)( 46,143)( 47,142)( 48,141)
( 49,150)( 50,149)( 51,152)( 52,151)( 53,146)( 54,145)( 55,148)( 56,147)
( 57,160)( 58,159)( 59,158)( 60,157)( 61,156)( 62,155)( 63,154)( 64,153)
( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)( 72,168)
( 73,172)( 74,171)( 75,170)( 76,169)( 77,176)( 78,175)( 79,174)( 80,173)
( 81,182)( 82,181)( 83,184)( 84,183)( 85,178)( 86,177)( 87,180)( 88,179)
( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,187)( 95,186)( 96,185)
(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)(200,296)
(201,300)(202,299)(203,298)(204,297)(205,304)(206,303)(207,302)(208,301)
(209,310)(210,309)(211,312)(212,311)(213,306)(214,305)(215,308)(216,307)
(217,320)(218,319)(219,318)(220,317)(221,316)(222,315)(223,314)(224,313)
(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)(232,328)
(233,332)(234,331)(235,330)(236,329)(237,336)(238,335)(239,334)(240,333)
(241,342)(242,341)(243,344)(244,343)(245,338)(246,337)(247,340)(248,339)
(249,352)(250,351)(251,350)(252,349)(253,348)(254,347)(255,346)(256,345)
(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)
(265,364)(266,363)(267,362)(268,361)(269,368)(270,367)(271,366)(272,365)
(273,374)(274,373)(275,376)(276,375)(277,370)(278,369)(279,372)(280,371)
(281,384)(282,383)(283,382)(284,381)(285,380)(286,379)(287,378)(288,377);;
s1 := ( 1,111)( 2,112)( 3,109)( 4,110)( 5,106)( 6,105)( 7,108)( 8,107)
( 9,102)( 10,101)( 11,104)( 12,103)( 13, 99)( 14,100)( 15, 97)( 16, 98)
( 17,113)( 18,114)( 19,115)( 20,116)( 21,120)( 22,119)( 23,118)( 24,117)
( 25,123)( 26,124)( 27,121)( 28,122)( 29,126)( 30,125)( 31,128)( 32,127)
( 33,175)( 34,176)( 35,173)( 36,174)( 37,170)( 38,169)( 39,172)( 40,171)
( 41,166)( 42,165)( 43,168)( 44,167)( 45,163)( 46,164)( 47,161)( 48,162)
( 49,177)( 50,178)( 51,179)( 52,180)( 53,184)( 54,183)( 55,182)( 56,181)
( 57,187)( 58,188)( 59,185)( 60,186)( 61,190)( 62,189)( 63,192)( 64,191)
( 65,143)( 66,144)( 67,141)( 68,142)( 69,138)( 70,137)( 71,140)( 72,139)
( 73,134)( 74,133)( 75,136)( 76,135)( 77,131)( 78,132)( 79,129)( 80,130)
( 81,145)( 82,146)( 83,147)( 84,148)( 85,152)( 86,151)( 87,150)( 88,149)
( 89,155)( 90,156)( 91,153)( 92,154)( 93,158)( 94,157)( 95,160)( 96,159)
(193,304)(194,303)(195,302)(196,301)(197,297)(198,298)(199,299)(200,300)
(201,293)(202,294)(203,295)(204,296)(205,292)(206,291)(207,290)(208,289)
(209,306)(210,305)(211,308)(212,307)(213,311)(214,312)(215,309)(216,310)
(217,316)(218,315)(219,314)(220,313)(221,317)(222,318)(223,319)(224,320)
(225,368)(226,367)(227,366)(228,365)(229,361)(230,362)(231,363)(232,364)
(233,357)(234,358)(235,359)(236,360)(237,356)(238,355)(239,354)(240,353)
(241,370)(242,369)(243,372)(244,371)(245,375)(246,376)(247,373)(248,374)
(249,380)(250,379)(251,378)(252,377)(253,381)(254,382)(255,383)(256,384)
(257,336)(258,335)(259,334)(260,333)(261,329)(262,330)(263,331)(264,332)
(265,325)(266,326)(267,327)(268,328)(269,324)(270,323)(271,322)(272,321)
(273,338)(274,337)(275,340)(276,339)(277,343)(278,344)(279,341)(280,342)
(281,348)(282,347)(283,346)(284,345)(285,349)(286,350)(287,351)(288,352);;
s2 := ( 1,161)( 2,162)( 3,165)( 4,166)( 5,163)( 6,164)( 7,167)( 8,168)
( 9,182)( 10,181)( 11,178)( 12,177)( 13,184)( 14,183)( 15,180)( 16,179)
( 17,172)( 18,171)( 19,176)( 20,175)( 21,170)( 22,169)( 23,174)( 24,173)
( 25,192)( 26,191)( 27,188)( 28,187)( 29,190)( 30,189)( 31,186)( 32,185)
( 33,129)( 34,130)( 35,133)( 36,134)( 37,131)( 38,132)( 39,135)( 40,136)
( 41,150)( 42,149)( 43,146)( 44,145)( 45,152)( 46,151)( 47,148)( 48,147)
( 49,140)( 50,139)( 51,144)( 52,143)( 53,138)( 54,137)( 55,142)( 56,141)
( 57,160)( 58,159)( 59,156)( 60,155)( 61,158)( 62,157)( 63,154)( 64,153)
( 65, 97)( 66, 98)( 67,101)( 68,102)( 69, 99)( 70,100)( 71,103)( 72,104)
( 73,118)( 74,117)( 75,114)( 76,113)( 77,120)( 78,119)( 79,116)( 80,115)
( 81,108)( 82,107)( 83,112)( 84,111)( 85,106)( 86,105)( 87,110)( 88,109)
( 89,128)( 90,127)( 91,124)( 92,123)( 93,126)( 94,125)( 95,122)( 96,121)
(193,354)(194,353)(195,358)(196,357)(197,356)(198,355)(199,360)(200,359)
(201,373)(202,374)(203,369)(204,370)(205,375)(206,376)(207,371)(208,372)
(209,363)(210,364)(211,367)(212,368)(213,361)(214,362)(215,365)(216,366)
(217,383)(218,384)(219,379)(220,380)(221,381)(222,382)(223,377)(224,378)
(225,322)(226,321)(227,326)(228,325)(229,324)(230,323)(231,328)(232,327)
(233,341)(234,342)(235,337)(236,338)(237,343)(238,344)(239,339)(240,340)
(241,331)(242,332)(243,335)(244,336)(245,329)(246,330)(247,333)(248,334)
(249,351)(250,352)(251,347)(252,348)(253,349)(254,350)(255,345)(256,346)
(257,290)(258,289)(259,294)(260,293)(261,292)(262,291)(263,296)(264,295)
(265,309)(266,310)(267,305)(268,306)(269,311)(270,312)(271,307)(272,308)
(273,299)(274,300)(275,303)(276,304)(277,297)(278,298)(279,301)(280,302)
(281,319)(282,320)(283,315)(284,316)(285,317)(286,318)(287,313)(288,314);;
s3 := ( 1,290)( 2,289)( 3,292)( 4,291)( 5,296)( 6,295)( 7,294)( 8,293)
( 9,299)( 10,300)( 11,297)( 12,298)( 13,301)( 14,302)( 15,303)( 16,304)
( 17,319)( 18,320)( 19,317)( 20,318)( 21,313)( 22,314)( 23,315)( 24,316)
( 25,309)( 26,310)( 27,311)( 28,312)( 29,307)( 30,308)( 31,305)( 32,306)
( 33,354)( 34,353)( 35,356)( 36,355)( 37,360)( 38,359)( 39,358)( 40,357)
( 41,363)( 42,364)( 43,361)( 44,362)( 45,365)( 46,366)( 47,367)( 48,368)
( 49,383)( 50,384)( 51,381)( 52,382)( 53,377)( 54,378)( 55,379)( 56,380)
( 57,373)( 58,374)( 59,375)( 60,376)( 61,371)( 62,372)( 63,369)( 64,370)
( 65,322)( 66,321)( 67,324)( 68,323)( 69,328)( 70,327)( 71,326)( 72,325)
( 73,331)( 74,332)( 75,329)( 76,330)( 77,333)( 78,334)( 79,335)( 80,336)
( 81,351)( 82,352)( 83,349)( 84,350)( 85,345)( 86,346)( 87,347)( 88,348)
( 89,341)( 90,342)( 91,343)( 92,344)( 93,339)( 94,340)( 95,337)( 96,338)
( 97,194)( 98,193)( 99,196)(100,195)(101,200)(102,199)(103,198)(104,197)
(105,203)(106,204)(107,201)(108,202)(109,205)(110,206)(111,207)(112,208)
(113,223)(114,224)(115,221)(116,222)(117,217)(118,218)(119,219)(120,220)
(121,213)(122,214)(123,215)(124,216)(125,211)(126,212)(127,209)(128,210)
(129,258)(130,257)(131,260)(132,259)(133,264)(134,263)(135,262)(136,261)
(137,267)(138,268)(139,265)(140,266)(141,269)(142,270)(143,271)(144,272)
(145,287)(146,288)(147,285)(148,286)(149,281)(150,282)(151,283)(152,284)
(153,277)(154,278)(155,279)(156,280)(157,275)(158,276)(159,273)(160,274)
(161,226)(162,225)(163,228)(164,227)(165,232)(166,231)(167,230)(168,229)
(169,235)(170,236)(171,233)(172,234)(173,237)(174,238)(175,239)(176,240)
(177,255)(178,256)(179,253)(180,254)(181,249)(182,250)(183,251)(184,252)
(185,245)(186,246)(187,247)(188,248)(189,243)(190,244)(191,241)(192,242);;
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, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2,
s3*s0*s2*s1*s3*s0*s2*s3*s1*s2*s3*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)
( 8,104)( 9,108)( 10,107)( 11,106)( 12,105)( 13,112)( 14,111)( 15,110)
( 16,109)( 17,118)( 18,117)( 19,120)( 20,119)( 21,114)( 22,113)( 23,116)
( 24,115)( 25,128)( 26,127)( 27,126)( 28,125)( 29,124)( 30,123)( 31,122)
( 32,121)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)
( 40,136)( 41,140)( 42,139)( 43,138)( 44,137)( 45,144)( 46,143)( 47,142)
( 48,141)( 49,150)( 50,149)( 51,152)( 52,151)( 53,146)( 54,145)( 55,148)
( 56,147)( 57,160)( 58,159)( 59,158)( 60,157)( 61,156)( 62,155)( 63,154)
( 64,153)( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)
( 72,168)( 73,172)( 74,171)( 75,170)( 76,169)( 77,176)( 78,175)( 79,174)
( 80,173)( 81,182)( 82,181)( 83,184)( 84,183)( 85,178)( 86,177)( 87,180)
( 88,179)( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,187)( 95,186)
( 96,185)(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)
(200,296)(201,300)(202,299)(203,298)(204,297)(205,304)(206,303)(207,302)
(208,301)(209,310)(210,309)(211,312)(212,311)(213,306)(214,305)(215,308)
(216,307)(217,320)(218,319)(219,318)(220,317)(221,316)(222,315)(223,314)
(224,313)(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)
(232,328)(233,332)(234,331)(235,330)(236,329)(237,336)(238,335)(239,334)
(240,333)(241,342)(242,341)(243,344)(244,343)(245,338)(246,337)(247,340)
(248,339)(249,352)(250,351)(251,350)(252,349)(253,348)(254,347)(255,346)
(256,345)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)
(264,360)(265,364)(266,363)(267,362)(268,361)(269,368)(270,367)(271,366)
(272,365)(273,374)(274,373)(275,376)(276,375)(277,370)(278,369)(279,372)
(280,371)(281,384)(282,383)(283,382)(284,381)(285,380)(286,379)(287,378)
(288,377);
s1 := Sym(384)!( 1,111)( 2,112)( 3,109)( 4,110)( 5,106)( 6,105)( 7,108)
( 8,107)( 9,102)( 10,101)( 11,104)( 12,103)( 13, 99)( 14,100)( 15, 97)
( 16, 98)( 17,113)( 18,114)( 19,115)( 20,116)( 21,120)( 22,119)( 23,118)
( 24,117)( 25,123)( 26,124)( 27,121)( 28,122)( 29,126)( 30,125)( 31,128)
( 32,127)( 33,175)( 34,176)( 35,173)( 36,174)( 37,170)( 38,169)( 39,172)
( 40,171)( 41,166)( 42,165)( 43,168)( 44,167)( 45,163)( 46,164)( 47,161)
( 48,162)( 49,177)( 50,178)( 51,179)( 52,180)( 53,184)( 54,183)( 55,182)
( 56,181)( 57,187)( 58,188)( 59,185)( 60,186)( 61,190)( 62,189)( 63,192)
( 64,191)( 65,143)( 66,144)( 67,141)( 68,142)( 69,138)( 70,137)( 71,140)
( 72,139)( 73,134)( 74,133)( 75,136)( 76,135)( 77,131)( 78,132)( 79,129)
( 80,130)( 81,145)( 82,146)( 83,147)( 84,148)( 85,152)( 86,151)( 87,150)
( 88,149)( 89,155)( 90,156)( 91,153)( 92,154)( 93,158)( 94,157)( 95,160)
( 96,159)(193,304)(194,303)(195,302)(196,301)(197,297)(198,298)(199,299)
(200,300)(201,293)(202,294)(203,295)(204,296)(205,292)(206,291)(207,290)
(208,289)(209,306)(210,305)(211,308)(212,307)(213,311)(214,312)(215,309)
(216,310)(217,316)(218,315)(219,314)(220,313)(221,317)(222,318)(223,319)
(224,320)(225,368)(226,367)(227,366)(228,365)(229,361)(230,362)(231,363)
(232,364)(233,357)(234,358)(235,359)(236,360)(237,356)(238,355)(239,354)
(240,353)(241,370)(242,369)(243,372)(244,371)(245,375)(246,376)(247,373)
(248,374)(249,380)(250,379)(251,378)(252,377)(253,381)(254,382)(255,383)
(256,384)(257,336)(258,335)(259,334)(260,333)(261,329)(262,330)(263,331)
(264,332)(265,325)(266,326)(267,327)(268,328)(269,324)(270,323)(271,322)
(272,321)(273,338)(274,337)(275,340)(276,339)(277,343)(278,344)(279,341)
(280,342)(281,348)(282,347)(283,346)(284,345)(285,349)(286,350)(287,351)
(288,352);
s2 := Sym(384)!( 1,161)( 2,162)( 3,165)( 4,166)( 5,163)( 6,164)( 7,167)
( 8,168)( 9,182)( 10,181)( 11,178)( 12,177)( 13,184)( 14,183)( 15,180)
( 16,179)( 17,172)( 18,171)( 19,176)( 20,175)( 21,170)( 22,169)( 23,174)
( 24,173)( 25,192)( 26,191)( 27,188)( 28,187)( 29,190)( 30,189)( 31,186)
( 32,185)( 33,129)( 34,130)( 35,133)( 36,134)( 37,131)( 38,132)( 39,135)
( 40,136)( 41,150)( 42,149)( 43,146)( 44,145)( 45,152)( 46,151)( 47,148)
( 48,147)( 49,140)( 50,139)( 51,144)( 52,143)( 53,138)( 54,137)( 55,142)
( 56,141)( 57,160)( 58,159)( 59,156)( 60,155)( 61,158)( 62,157)( 63,154)
( 64,153)( 65, 97)( 66, 98)( 67,101)( 68,102)( 69, 99)( 70,100)( 71,103)
( 72,104)( 73,118)( 74,117)( 75,114)( 76,113)( 77,120)( 78,119)( 79,116)
( 80,115)( 81,108)( 82,107)( 83,112)( 84,111)( 85,106)( 86,105)( 87,110)
( 88,109)( 89,128)( 90,127)( 91,124)( 92,123)( 93,126)( 94,125)( 95,122)
( 96,121)(193,354)(194,353)(195,358)(196,357)(197,356)(198,355)(199,360)
(200,359)(201,373)(202,374)(203,369)(204,370)(205,375)(206,376)(207,371)
(208,372)(209,363)(210,364)(211,367)(212,368)(213,361)(214,362)(215,365)
(216,366)(217,383)(218,384)(219,379)(220,380)(221,381)(222,382)(223,377)
(224,378)(225,322)(226,321)(227,326)(228,325)(229,324)(230,323)(231,328)
(232,327)(233,341)(234,342)(235,337)(236,338)(237,343)(238,344)(239,339)
(240,340)(241,331)(242,332)(243,335)(244,336)(245,329)(246,330)(247,333)
(248,334)(249,351)(250,352)(251,347)(252,348)(253,349)(254,350)(255,345)
(256,346)(257,290)(258,289)(259,294)(260,293)(261,292)(262,291)(263,296)
(264,295)(265,309)(266,310)(267,305)(268,306)(269,311)(270,312)(271,307)
(272,308)(273,299)(274,300)(275,303)(276,304)(277,297)(278,298)(279,301)
(280,302)(281,319)(282,320)(283,315)(284,316)(285,317)(286,318)(287,313)
(288,314);
s3 := Sym(384)!( 1,290)( 2,289)( 3,292)( 4,291)( 5,296)( 6,295)( 7,294)
( 8,293)( 9,299)( 10,300)( 11,297)( 12,298)( 13,301)( 14,302)( 15,303)
( 16,304)( 17,319)( 18,320)( 19,317)( 20,318)( 21,313)( 22,314)( 23,315)
( 24,316)( 25,309)( 26,310)( 27,311)( 28,312)( 29,307)( 30,308)( 31,305)
( 32,306)( 33,354)( 34,353)( 35,356)( 36,355)( 37,360)( 38,359)( 39,358)
( 40,357)( 41,363)( 42,364)( 43,361)( 44,362)( 45,365)( 46,366)( 47,367)
( 48,368)( 49,383)( 50,384)( 51,381)( 52,382)( 53,377)( 54,378)( 55,379)
( 56,380)( 57,373)( 58,374)( 59,375)( 60,376)( 61,371)( 62,372)( 63,369)
( 64,370)( 65,322)( 66,321)( 67,324)( 68,323)( 69,328)( 70,327)( 71,326)
( 72,325)( 73,331)( 74,332)( 75,329)( 76,330)( 77,333)( 78,334)( 79,335)
( 80,336)( 81,351)( 82,352)( 83,349)( 84,350)( 85,345)( 86,346)( 87,347)
( 88,348)( 89,341)( 90,342)( 91,343)( 92,344)( 93,339)( 94,340)( 95,337)
( 96,338)( 97,194)( 98,193)( 99,196)(100,195)(101,200)(102,199)(103,198)
(104,197)(105,203)(106,204)(107,201)(108,202)(109,205)(110,206)(111,207)
(112,208)(113,223)(114,224)(115,221)(116,222)(117,217)(118,218)(119,219)
(120,220)(121,213)(122,214)(123,215)(124,216)(125,211)(126,212)(127,209)
(128,210)(129,258)(130,257)(131,260)(132,259)(133,264)(134,263)(135,262)
(136,261)(137,267)(138,268)(139,265)(140,266)(141,269)(142,270)(143,271)
(144,272)(145,287)(146,288)(147,285)(148,286)(149,281)(150,282)(151,283)
(152,284)(153,277)(154,278)(155,279)(156,280)(157,275)(158,276)(159,273)
(160,274)(161,226)(162,225)(163,228)(164,227)(165,232)(166,231)(167,230)
(168,229)(169,235)(170,236)(171,233)(172,234)(173,237)(174,238)(175,239)
(176,240)(177,255)(178,256)(179,253)(180,254)(181,249)(182,250)(183,251)
(184,252)(185,245)(186,246)(187,247)(188,248)(189,243)(190,244)(191,241)
(192,242);
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,
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2,
s3*s0*s2*s1*s3*s0*s2*s3*s1*s2*s3*s0*s1*s2*s0*s1 >;
References : None.
to this polytope