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