Polytope of Type {12,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,4}*768b
if this polytope has a name.
Group : SmallGroup(768,1089307)
Rank : 4
Schlafli Type : {12,6,4}
Number of vertices, edges, etc : 16, 48, 16, 4
Order of s0s1s2s3 : 8
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}*384b
4-fold quotients : {3,6,4}*192, {12,3,2}*192, {6,6,2}*192
8-fold quotients : {3,6,2}*96, {6,3,2}*96
16-fold quotients : {3,3,2}*48
24-fold quotients : {2,2,4}*32
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)
( 14, 24)( 15, 21)( 16, 22)( 27, 28)( 29, 31)( 30, 32)( 33, 41)( 34, 42)
( 35, 44)( 36, 43)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 51, 52)( 53, 55)
( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)( 63, 69)
( 64, 70)( 75, 76)( 77, 79)( 78, 80)( 81, 89)( 82, 90)( 83, 92)( 84, 91)
( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 99,100)(101,103)(102,104)(105,113)
(106,114)(107,116)(108,115)(109,119)(110,120)(111,117)(112,118)(123,124)
(125,127)(126,128)(129,137)(130,138)(131,140)(132,139)(133,143)(134,144)
(135,141)(136,142)(147,148)(149,151)(150,152)(153,161)(154,162)(155,164)
(156,163)(157,167)(158,168)(159,165)(160,166)(171,172)(173,175)(174,176)
(177,185)(178,186)(179,188)(180,187)(181,191)(182,192)(183,189)(184,190)
(193,194)(197,200)(198,199)(201,210)(202,209)(203,211)(204,212)(205,216)
(206,215)(207,214)(208,213)(217,218)(221,224)(222,223)(225,234)(226,233)
(227,235)(228,236)(229,240)(230,239)(231,238)(232,237)(241,242)(245,248)
(246,247)(249,258)(250,257)(251,259)(252,260)(253,264)(254,263)(255,262)
(256,261)(265,266)(269,272)(270,271)(273,282)(274,281)(275,283)(276,284)
(277,288)(278,287)(279,286)(280,285)(289,290)(293,296)(294,295)(297,306)
(298,305)(299,307)(300,308)(301,312)(302,311)(303,310)(304,309)(313,314)
(317,320)(318,319)(321,330)(322,329)(323,331)(324,332)(325,336)(326,335)
(327,334)(328,333)(337,338)(341,344)(342,343)(345,354)(346,353)(347,355)
(348,356)(349,360)(350,359)(351,358)(352,357)(361,362)(365,368)(366,367)
(369,378)(370,377)(371,379)(372,380)(373,384)(374,383)(375,382)(376,381);;
s1 := ( 1,209)( 2,210)( 3,214)( 4,213)( 5,212)( 6,211)( 7,216)( 8,215)
( 9,201)( 10,202)( 11,206)( 12,205)( 13,204)( 14,203)( 15,208)( 16,207)
( 17,193)( 18,194)( 19,198)( 20,197)( 21,196)( 22,195)( 23,200)( 24,199)
( 25,233)( 26,234)( 27,238)( 28,237)( 29,236)( 30,235)( 31,240)( 32,239)
( 33,225)( 34,226)( 35,230)( 36,229)( 37,228)( 38,227)( 39,232)( 40,231)
( 41,217)( 42,218)( 43,222)( 44,221)( 45,220)( 46,219)( 47,224)( 48,223)
( 49,257)( 50,258)( 51,262)( 52,261)( 53,260)( 54,259)( 55,264)( 56,263)
( 57,249)( 58,250)( 59,254)( 60,253)( 61,252)( 62,251)( 63,256)( 64,255)
( 65,241)( 66,242)( 67,246)( 68,245)( 69,244)( 70,243)( 71,248)( 72,247)
( 73,281)( 74,282)( 75,286)( 76,285)( 77,284)( 78,283)( 79,288)( 80,287)
( 81,273)( 82,274)( 83,278)( 84,277)( 85,276)( 86,275)( 87,280)( 88,279)
( 89,265)( 90,266)( 91,270)( 92,269)( 93,268)( 94,267)( 95,272)( 96,271)
( 97,305)( 98,306)( 99,310)(100,309)(101,308)(102,307)(103,312)(104,311)
(105,297)(106,298)(107,302)(108,301)(109,300)(110,299)(111,304)(112,303)
(113,289)(114,290)(115,294)(116,293)(117,292)(118,291)(119,296)(120,295)
(121,329)(122,330)(123,334)(124,333)(125,332)(126,331)(127,336)(128,335)
(129,321)(130,322)(131,326)(132,325)(133,324)(134,323)(135,328)(136,327)
(137,313)(138,314)(139,318)(140,317)(141,316)(142,315)(143,320)(144,319)
(145,353)(146,354)(147,358)(148,357)(149,356)(150,355)(151,360)(152,359)
(153,345)(154,346)(155,350)(156,349)(157,348)(158,347)(159,352)(160,351)
(161,337)(162,338)(163,342)(164,341)(165,340)(166,339)(167,344)(168,343)
(169,377)(170,378)(171,382)(172,381)(173,380)(174,379)(175,384)(176,383)
(177,369)(178,370)(179,374)(180,373)(181,372)(182,371)(183,376)(184,375)
(185,361)(186,362)(187,366)(188,365)(189,364)(190,363)(191,368)(192,367);;
s2 := ( 1,291)( 2,292)( 3,289)( 4,290)( 5,294)( 6,293)( 7,295)( 8,296)
( 9,307)( 10,308)( 11,305)( 12,306)( 13,310)( 14,309)( 15,311)( 16,312)
( 17,299)( 18,300)( 19,297)( 20,298)( 21,302)( 22,301)( 23,303)( 24,304)
( 25,315)( 26,316)( 27,313)( 28,314)( 29,318)( 30,317)( 31,319)( 32,320)
( 33,331)( 34,332)( 35,329)( 36,330)( 37,334)( 38,333)( 39,335)( 40,336)
( 41,323)( 42,324)( 43,321)( 44,322)( 45,326)( 46,325)( 47,327)( 48,328)
( 49,363)( 50,364)( 51,361)( 52,362)( 53,366)( 54,365)( 55,367)( 56,368)
( 57,379)( 58,380)( 59,377)( 60,378)( 61,382)( 62,381)( 63,383)( 64,384)
( 65,371)( 66,372)( 67,369)( 68,370)( 69,374)( 70,373)( 71,375)( 72,376)
( 73,339)( 74,340)( 75,337)( 76,338)( 77,342)( 78,341)( 79,343)( 80,344)
( 81,355)( 82,356)( 83,353)( 84,354)( 85,358)( 86,357)( 87,359)( 88,360)
( 89,347)( 90,348)( 91,345)( 92,346)( 93,350)( 94,349)( 95,351)( 96,352)
( 97,195)( 98,196)( 99,193)(100,194)(101,198)(102,197)(103,199)(104,200)
(105,211)(106,212)(107,209)(108,210)(109,214)(110,213)(111,215)(112,216)
(113,203)(114,204)(115,201)(116,202)(117,206)(118,205)(119,207)(120,208)
(121,219)(122,220)(123,217)(124,218)(125,222)(126,221)(127,223)(128,224)
(129,235)(130,236)(131,233)(132,234)(133,238)(134,237)(135,239)(136,240)
(137,227)(138,228)(139,225)(140,226)(141,230)(142,229)(143,231)(144,232)
(145,267)(146,268)(147,265)(148,266)(149,270)(150,269)(151,271)(152,272)
(153,283)(154,284)(155,281)(156,282)(157,286)(158,285)(159,287)(160,288)
(161,275)(162,276)(163,273)(164,274)(165,278)(166,277)(167,279)(168,280)
(169,243)(170,244)(171,241)(172,242)(173,246)(174,245)(175,247)(176,248)
(177,259)(178,260)(179,257)(180,258)(181,262)(182,261)(183,263)(184,264)
(185,251)(186,252)(187,249)(188,250)(189,254)(190,253)(191,255)(192,256);;
s3 := ( 1, 49)( 2, 50)( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)
( 9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 63)( 16, 64)
( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)( 24, 72)
( 25, 73)( 26, 74)( 27, 75)( 28, 76)( 29, 77)( 30, 78)( 31, 79)( 32, 80)
( 33, 81)( 34, 82)( 35, 83)( 36, 84)( 37, 85)( 38, 86)( 39, 87)( 40, 88)
( 41, 89)( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)
( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)
(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)(112,160)
(113,161)(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)(120,168)
(121,169)(122,170)(123,171)(124,172)(125,173)(126,174)(127,175)(128,176)
(129,177)(130,178)(131,179)(132,180)(133,181)(134,182)(135,183)(136,184)
(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192)
(193,241)(194,242)(195,243)(196,244)(197,245)(198,246)(199,247)(200,248)
(201,249)(202,250)(203,251)(204,252)(205,253)(206,254)(207,255)(208,256)
(209,257)(210,258)(211,259)(212,260)(213,261)(214,262)(215,263)(216,264)
(217,265)(218,266)(219,267)(220,268)(221,269)(222,270)(223,271)(224,272)
(225,273)(226,274)(227,275)(228,276)(229,277)(230,278)(231,279)(232,280)
(233,281)(234,282)(235,283)(236,284)(237,285)(238,286)(239,287)(240,288)
(289,337)(290,338)(291,339)(292,340)(293,341)(294,342)(295,343)(296,344)
(297,345)(298,346)(299,347)(300,348)(301,349)(302,350)(303,351)(304,352)
(305,353)(306,354)(307,355)(308,356)(309,357)(310,358)(311,359)(312,360)
(313,361)(314,362)(315,363)(316,364)(317,365)(318,366)(319,367)(320,368)
(321,369)(322,370)(323,371)(324,372)(325,373)(326,374)(327,375)(328,376)
(329,377)(330,378)(331,379)(332,380)(333,381)(334,382)(335,383)(336,384);;
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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)
( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 27, 28)( 29, 31)( 30, 32)( 33, 41)
( 34, 42)( 35, 44)( 36, 43)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 51, 52)
( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)
( 63, 69)( 64, 70)( 75, 76)( 77, 79)( 78, 80)( 81, 89)( 82, 90)( 83, 92)
( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 99,100)(101,103)(102,104)
(105,113)(106,114)(107,116)(108,115)(109,119)(110,120)(111,117)(112,118)
(123,124)(125,127)(126,128)(129,137)(130,138)(131,140)(132,139)(133,143)
(134,144)(135,141)(136,142)(147,148)(149,151)(150,152)(153,161)(154,162)
(155,164)(156,163)(157,167)(158,168)(159,165)(160,166)(171,172)(173,175)
(174,176)(177,185)(178,186)(179,188)(180,187)(181,191)(182,192)(183,189)
(184,190)(193,194)(197,200)(198,199)(201,210)(202,209)(203,211)(204,212)
(205,216)(206,215)(207,214)(208,213)(217,218)(221,224)(222,223)(225,234)
(226,233)(227,235)(228,236)(229,240)(230,239)(231,238)(232,237)(241,242)
(245,248)(246,247)(249,258)(250,257)(251,259)(252,260)(253,264)(254,263)
(255,262)(256,261)(265,266)(269,272)(270,271)(273,282)(274,281)(275,283)
(276,284)(277,288)(278,287)(279,286)(280,285)(289,290)(293,296)(294,295)
(297,306)(298,305)(299,307)(300,308)(301,312)(302,311)(303,310)(304,309)
(313,314)(317,320)(318,319)(321,330)(322,329)(323,331)(324,332)(325,336)
(326,335)(327,334)(328,333)(337,338)(341,344)(342,343)(345,354)(346,353)
(347,355)(348,356)(349,360)(350,359)(351,358)(352,357)(361,362)(365,368)
(366,367)(369,378)(370,377)(371,379)(372,380)(373,384)(374,383)(375,382)
(376,381);
s1 := Sym(384)!( 1,209)( 2,210)( 3,214)( 4,213)( 5,212)( 6,211)( 7,216)
( 8,215)( 9,201)( 10,202)( 11,206)( 12,205)( 13,204)( 14,203)( 15,208)
( 16,207)( 17,193)( 18,194)( 19,198)( 20,197)( 21,196)( 22,195)( 23,200)
( 24,199)( 25,233)( 26,234)( 27,238)( 28,237)( 29,236)( 30,235)( 31,240)
( 32,239)( 33,225)( 34,226)( 35,230)( 36,229)( 37,228)( 38,227)( 39,232)
( 40,231)( 41,217)( 42,218)( 43,222)( 44,221)( 45,220)( 46,219)( 47,224)
( 48,223)( 49,257)( 50,258)( 51,262)( 52,261)( 53,260)( 54,259)( 55,264)
( 56,263)( 57,249)( 58,250)( 59,254)( 60,253)( 61,252)( 62,251)( 63,256)
( 64,255)( 65,241)( 66,242)( 67,246)( 68,245)( 69,244)( 70,243)( 71,248)
( 72,247)( 73,281)( 74,282)( 75,286)( 76,285)( 77,284)( 78,283)( 79,288)
( 80,287)( 81,273)( 82,274)( 83,278)( 84,277)( 85,276)( 86,275)( 87,280)
( 88,279)( 89,265)( 90,266)( 91,270)( 92,269)( 93,268)( 94,267)( 95,272)
( 96,271)( 97,305)( 98,306)( 99,310)(100,309)(101,308)(102,307)(103,312)
(104,311)(105,297)(106,298)(107,302)(108,301)(109,300)(110,299)(111,304)
(112,303)(113,289)(114,290)(115,294)(116,293)(117,292)(118,291)(119,296)
(120,295)(121,329)(122,330)(123,334)(124,333)(125,332)(126,331)(127,336)
(128,335)(129,321)(130,322)(131,326)(132,325)(133,324)(134,323)(135,328)
(136,327)(137,313)(138,314)(139,318)(140,317)(141,316)(142,315)(143,320)
(144,319)(145,353)(146,354)(147,358)(148,357)(149,356)(150,355)(151,360)
(152,359)(153,345)(154,346)(155,350)(156,349)(157,348)(158,347)(159,352)
(160,351)(161,337)(162,338)(163,342)(164,341)(165,340)(166,339)(167,344)
(168,343)(169,377)(170,378)(171,382)(172,381)(173,380)(174,379)(175,384)
(176,383)(177,369)(178,370)(179,374)(180,373)(181,372)(182,371)(183,376)
(184,375)(185,361)(186,362)(187,366)(188,365)(189,364)(190,363)(191,368)
(192,367);
s2 := Sym(384)!( 1,291)( 2,292)( 3,289)( 4,290)( 5,294)( 6,293)( 7,295)
( 8,296)( 9,307)( 10,308)( 11,305)( 12,306)( 13,310)( 14,309)( 15,311)
( 16,312)( 17,299)( 18,300)( 19,297)( 20,298)( 21,302)( 22,301)( 23,303)
( 24,304)( 25,315)( 26,316)( 27,313)( 28,314)( 29,318)( 30,317)( 31,319)
( 32,320)( 33,331)( 34,332)( 35,329)( 36,330)( 37,334)( 38,333)( 39,335)
( 40,336)( 41,323)( 42,324)( 43,321)( 44,322)( 45,326)( 46,325)( 47,327)
( 48,328)( 49,363)( 50,364)( 51,361)( 52,362)( 53,366)( 54,365)( 55,367)
( 56,368)( 57,379)( 58,380)( 59,377)( 60,378)( 61,382)( 62,381)( 63,383)
( 64,384)( 65,371)( 66,372)( 67,369)( 68,370)( 69,374)( 70,373)( 71,375)
( 72,376)( 73,339)( 74,340)( 75,337)( 76,338)( 77,342)( 78,341)( 79,343)
( 80,344)( 81,355)( 82,356)( 83,353)( 84,354)( 85,358)( 86,357)( 87,359)
( 88,360)( 89,347)( 90,348)( 91,345)( 92,346)( 93,350)( 94,349)( 95,351)
( 96,352)( 97,195)( 98,196)( 99,193)(100,194)(101,198)(102,197)(103,199)
(104,200)(105,211)(106,212)(107,209)(108,210)(109,214)(110,213)(111,215)
(112,216)(113,203)(114,204)(115,201)(116,202)(117,206)(118,205)(119,207)
(120,208)(121,219)(122,220)(123,217)(124,218)(125,222)(126,221)(127,223)
(128,224)(129,235)(130,236)(131,233)(132,234)(133,238)(134,237)(135,239)
(136,240)(137,227)(138,228)(139,225)(140,226)(141,230)(142,229)(143,231)
(144,232)(145,267)(146,268)(147,265)(148,266)(149,270)(150,269)(151,271)
(152,272)(153,283)(154,284)(155,281)(156,282)(157,286)(158,285)(159,287)
(160,288)(161,275)(162,276)(163,273)(164,274)(165,278)(166,277)(167,279)
(168,280)(169,243)(170,244)(171,241)(172,242)(173,246)(174,245)(175,247)
(176,248)(177,259)(178,260)(179,257)(180,258)(181,262)(182,261)(183,263)
(184,264)(185,251)(186,252)(187,249)(188,250)(189,254)(190,253)(191,255)
(192,256);
s3 := Sym(384)!( 1, 49)( 2, 50)( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)
( 8, 56)( 9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 63)
( 16, 64)( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)
( 24, 72)( 25, 73)( 26, 74)( 27, 75)( 28, 76)( 29, 77)( 30, 78)( 31, 79)
( 32, 80)( 33, 81)( 34, 82)( 35, 83)( 36, 84)( 37, 85)( 38, 86)( 39, 87)
( 40, 88)( 41, 89)( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)
( 48, 96)( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)
(104,152)(105,153)(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)
(112,160)(113,161)(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)
(120,168)(121,169)(122,170)(123,171)(124,172)(125,173)(126,174)(127,175)
(128,176)(129,177)(130,178)(131,179)(132,180)(133,181)(134,182)(135,183)
(136,184)(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)
(144,192)(193,241)(194,242)(195,243)(196,244)(197,245)(198,246)(199,247)
(200,248)(201,249)(202,250)(203,251)(204,252)(205,253)(206,254)(207,255)
(208,256)(209,257)(210,258)(211,259)(212,260)(213,261)(214,262)(215,263)
(216,264)(217,265)(218,266)(219,267)(220,268)(221,269)(222,270)(223,271)
(224,272)(225,273)(226,274)(227,275)(228,276)(229,277)(230,278)(231,279)
(232,280)(233,281)(234,282)(235,283)(236,284)(237,285)(238,286)(239,287)
(240,288)(289,337)(290,338)(291,339)(292,340)(293,341)(294,342)(295,343)
(296,344)(297,345)(298,346)(299,347)(300,348)(301,349)(302,350)(303,351)
(304,352)(305,353)(306,354)(307,355)(308,356)(309,357)(310,358)(311,359)
(312,360)(313,361)(314,362)(315,363)(316,364)(317,365)(318,366)(319,367)
(320,368)(321,369)(322,370)(323,371)(324,372)(325,373)(326,374)(327,375)
(328,376)(329,377)(330,378)(331,379)(332,380)(333,381)(334,382)(335,383)
(336,384);
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,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope