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