Polytope of Type {12,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,4}*768e
if this polytope has a name.
Group : SmallGroup(768,1088766)
Rank : 4
Schlafli Type : {12,4,4}
Number of vertices, edges, etc : 24, 48, 16, 4
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 : {12,4,2}*384b, {6,4,4}*384d
4-fold quotients : {12,2,4}*192, {12,4,2}*192b, {12,4,2}*192c, {3,4,4}*192b, {6,4,2}*192
8-fold quotients : {12,2,2}*96, {6,2,4}*96, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
12-fold quotients : {4,2,4}*64
16-fold quotients : {3,2,4}*48, {3,4,2}*48, {6,2,2}*48
24-fold quotients : {2,2,4}*32, {4,2,2}*32
32-fold quotients : {3,2,2}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)
( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 39, 40)
( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 53, 57)( 54, 58)( 55, 60)
( 56, 59)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 75, 76)( 77, 81)
( 78, 82)( 79, 84)( 80, 83)( 87, 88)( 89, 93)( 90, 94)( 91, 96)( 92, 95)
( 99,100)(101,105)(102,106)(103,108)(104,107)(111,112)(113,117)(114,118)
(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)
(137,141)(138,142)(139,144)(140,143)(147,148)(149,153)(150,154)(151,156)
(152,155)(159,160)(161,165)(162,166)(163,168)(164,167)(171,172)(173,177)
(174,178)(175,180)(176,179)(183,184)(185,189)(186,190)(187,192)(188,191)
(193,205)(194,206)(195,208)(196,207)(197,213)(198,214)(199,216)(200,215)
(201,209)(202,210)(203,212)(204,211)(217,229)(218,230)(219,232)(220,231)
(221,237)(222,238)(223,240)(224,239)(225,233)(226,234)(227,236)(228,235)
(241,253)(242,254)(243,256)(244,255)(245,261)(246,262)(247,264)(248,263)
(249,257)(250,258)(251,260)(252,259)(265,277)(266,278)(267,280)(268,279)
(269,285)(270,286)(271,288)(272,287)(273,281)(274,282)(275,284)(276,283)
(289,301)(290,302)(291,304)(292,303)(293,309)(294,310)(295,312)(296,311)
(297,305)(298,306)(299,308)(300,307)(313,325)(314,326)(315,328)(316,327)
(317,333)(318,334)(319,336)(320,335)(321,329)(322,330)(323,332)(324,331)
(337,349)(338,350)(339,352)(340,351)(341,357)(342,358)(343,360)(344,359)
(345,353)(346,354)(347,356)(348,355)(361,373)(362,374)(363,376)(364,375)
(365,381)(366,382)(367,384)(368,383)(369,377)(370,378)(371,380)(372,379);;
s1 := ( 1,213)( 2,215)( 3,214)( 4,216)( 5,209)( 6,211)( 7,210)( 8,212)
( 9,205)( 10,207)( 11,206)( 12,208)( 13,201)( 14,203)( 15,202)( 16,204)
( 17,197)( 18,199)( 19,198)( 20,200)( 21,193)( 22,195)( 23,194)( 24,196)
( 25,237)( 26,239)( 27,238)( 28,240)( 29,233)( 30,235)( 31,234)( 32,236)
( 33,229)( 34,231)( 35,230)( 36,232)( 37,225)( 38,227)( 39,226)( 40,228)
( 41,221)( 42,223)( 43,222)( 44,224)( 45,217)( 46,219)( 47,218)( 48,220)
( 49,261)( 50,263)( 51,262)( 52,264)( 53,257)( 54,259)( 55,258)( 56,260)
( 57,253)( 58,255)( 59,254)( 60,256)( 61,249)( 62,251)( 63,250)( 64,252)
( 65,245)( 66,247)( 67,246)( 68,248)( 69,241)( 70,243)( 71,242)( 72,244)
( 73,285)( 74,287)( 75,286)( 76,288)( 77,281)( 78,283)( 79,282)( 80,284)
( 81,277)( 82,279)( 83,278)( 84,280)( 85,273)( 86,275)( 87,274)( 88,276)
( 89,269)( 90,271)( 91,270)( 92,272)( 93,265)( 94,267)( 95,266)( 96,268)
( 97,309)( 98,311)( 99,310)(100,312)(101,305)(102,307)(103,306)(104,308)
(105,301)(106,303)(107,302)(108,304)(109,297)(110,299)(111,298)(112,300)
(113,293)(114,295)(115,294)(116,296)(117,289)(118,291)(119,290)(120,292)
(121,333)(122,335)(123,334)(124,336)(125,329)(126,331)(127,330)(128,332)
(129,325)(130,327)(131,326)(132,328)(133,321)(134,323)(135,322)(136,324)
(137,317)(138,319)(139,318)(140,320)(141,313)(142,315)(143,314)(144,316)
(145,357)(146,359)(147,358)(148,360)(149,353)(150,355)(151,354)(152,356)
(153,349)(154,351)(155,350)(156,352)(157,345)(158,347)(159,346)(160,348)
(161,341)(162,343)(163,342)(164,344)(165,337)(166,339)(167,338)(168,340)
(169,381)(170,383)(171,382)(172,384)(173,377)(174,379)(175,378)(176,380)
(177,373)(178,375)(179,374)(180,376)(181,369)(182,371)(183,370)(184,372)
(185,365)(186,367)(187,366)(188,368)(189,361)(190,363)(191,362)(192,364);;
s2 := ( 1, 98)( 2, 97)( 3,100)( 4, 99)( 5,102)( 6,101)( 7,104)( 8,103)
( 9,106)( 10,105)( 11,108)( 12,107)( 13,110)( 14,109)( 15,112)( 16,111)
( 17,114)( 18,113)( 19,116)( 20,115)( 21,118)( 22,117)( 23,120)( 24,119)
( 25,122)( 26,121)( 27,124)( 28,123)( 29,126)( 30,125)( 31,128)( 32,127)
( 33,130)( 34,129)( 35,132)( 36,131)( 37,134)( 38,133)( 39,136)( 40,135)
( 41,138)( 42,137)( 43,140)( 44,139)( 45,142)( 46,141)( 47,144)( 48,143)
( 49,170)( 50,169)( 51,172)( 52,171)( 53,174)( 54,173)( 55,176)( 56,175)
( 57,178)( 58,177)( 59,180)( 60,179)( 61,182)( 62,181)( 63,184)( 64,183)
( 65,186)( 66,185)( 67,188)( 68,187)( 69,190)( 70,189)( 71,192)( 72,191)
( 73,146)( 74,145)( 75,148)( 76,147)( 77,150)( 78,149)( 79,152)( 80,151)
( 81,154)( 82,153)( 83,156)( 84,155)( 85,158)( 86,157)( 87,160)( 88,159)
( 89,162)( 90,161)( 91,164)( 92,163)( 93,166)( 94,165)( 95,168)( 96,167)
(193,290)(194,289)(195,292)(196,291)(197,294)(198,293)(199,296)(200,295)
(201,298)(202,297)(203,300)(204,299)(205,302)(206,301)(207,304)(208,303)
(209,306)(210,305)(211,308)(212,307)(213,310)(214,309)(215,312)(216,311)
(217,314)(218,313)(219,316)(220,315)(221,318)(222,317)(223,320)(224,319)
(225,322)(226,321)(227,324)(228,323)(229,326)(230,325)(231,328)(232,327)
(233,330)(234,329)(235,332)(236,331)(237,334)(238,333)(239,336)(240,335)
(241,362)(242,361)(243,364)(244,363)(245,366)(246,365)(247,368)(248,367)
(249,370)(250,369)(251,372)(252,371)(253,374)(254,373)(255,376)(256,375)
(257,378)(258,377)(259,380)(260,379)(261,382)(262,381)(263,384)(264,383)
(265,338)(266,337)(267,340)(268,339)(269,342)(270,341)(271,344)(272,343)
(273,346)(274,345)(275,348)(276,347)(277,350)(278,349)(279,352)(280,351)
(281,354)(282,353)(283,356)(284,355)(285,358)(286,357)(287,360)(288,359);;
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*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)
( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)
( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 53, 57)( 54, 58)
( 55, 60)( 56, 59)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 75, 76)
( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 87, 88)( 89, 93)( 90, 94)( 91, 96)
( 92, 95)( 99,100)(101,105)(102,106)(103,108)(104,107)(111,112)(113,117)
(114,118)(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)
(135,136)(137,141)(138,142)(139,144)(140,143)(147,148)(149,153)(150,154)
(151,156)(152,155)(159,160)(161,165)(162,166)(163,168)(164,167)(171,172)
(173,177)(174,178)(175,180)(176,179)(183,184)(185,189)(186,190)(187,192)
(188,191)(193,205)(194,206)(195,208)(196,207)(197,213)(198,214)(199,216)
(200,215)(201,209)(202,210)(203,212)(204,211)(217,229)(218,230)(219,232)
(220,231)(221,237)(222,238)(223,240)(224,239)(225,233)(226,234)(227,236)
(228,235)(241,253)(242,254)(243,256)(244,255)(245,261)(246,262)(247,264)
(248,263)(249,257)(250,258)(251,260)(252,259)(265,277)(266,278)(267,280)
(268,279)(269,285)(270,286)(271,288)(272,287)(273,281)(274,282)(275,284)
(276,283)(289,301)(290,302)(291,304)(292,303)(293,309)(294,310)(295,312)
(296,311)(297,305)(298,306)(299,308)(300,307)(313,325)(314,326)(315,328)
(316,327)(317,333)(318,334)(319,336)(320,335)(321,329)(322,330)(323,332)
(324,331)(337,349)(338,350)(339,352)(340,351)(341,357)(342,358)(343,360)
(344,359)(345,353)(346,354)(347,356)(348,355)(361,373)(362,374)(363,376)
(364,375)(365,381)(366,382)(367,384)(368,383)(369,377)(370,378)(371,380)
(372,379);
s1 := Sym(384)!( 1,213)( 2,215)( 3,214)( 4,216)( 5,209)( 6,211)( 7,210)
( 8,212)( 9,205)( 10,207)( 11,206)( 12,208)( 13,201)( 14,203)( 15,202)
( 16,204)( 17,197)( 18,199)( 19,198)( 20,200)( 21,193)( 22,195)( 23,194)
( 24,196)( 25,237)( 26,239)( 27,238)( 28,240)( 29,233)( 30,235)( 31,234)
( 32,236)( 33,229)( 34,231)( 35,230)( 36,232)( 37,225)( 38,227)( 39,226)
( 40,228)( 41,221)( 42,223)( 43,222)( 44,224)( 45,217)( 46,219)( 47,218)
( 48,220)( 49,261)( 50,263)( 51,262)( 52,264)( 53,257)( 54,259)( 55,258)
( 56,260)( 57,253)( 58,255)( 59,254)( 60,256)( 61,249)( 62,251)( 63,250)
( 64,252)( 65,245)( 66,247)( 67,246)( 68,248)( 69,241)( 70,243)( 71,242)
( 72,244)( 73,285)( 74,287)( 75,286)( 76,288)( 77,281)( 78,283)( 79,282)
( 80,284)( 81,277)( 82,279)( 83,278)( 84,280)( 85,273)( 86,275)( 87,274)
( 88,276)( 89,269)( 90,271)( 91,270)( 92,272)( 93,265)( 94,267)( 95,266)
( 96,268)( 97,309)( 98,311)( 99,310)(100,312)(101,305)(102,307)(103,306)
(104,308)(105,301)(106,303)(107,302)(108,304)(109,297)(110,299)(111,298)
(112,300)(113,293)(114,295)(115,294)(116,296)(117,289)(118,291)(119,290)
(120,292)(121,333)(122,335)(123,334)(124,336)(125,329)(126,331)(127,330)
(128,332)(129,325)(130,327)(131,326)(132,328)(133,321)(134,323)(135,322)
(136,324)(137,317)(138,319)(139,318)(140,320)(141,313)(142,315)(143,314)
(144,316)(145,357)(146,359)(147,358)(148,360)(149,353)(150,355)(151,354)
(152,356)(153,349)(154,351)(155,350)(156,352)(157,345)(158,347)(159,346)
(160,348)(161,341)(162,343)(163,342)(164,344)(165,337)(166,339)(167,338)
(168,340)(169,381)(170,383)(171,382)(172,384)(173,377)(174,379)(175,378)
(176,380)(177,373)(178,375)(179,374)(180,376)(181,369)(182,371)(183,370)
(184,372)(185,365)(186,367)(187,366)(188,368)(189,361)(190,363)(191,362)
(192,364);
s2 := Sym(384)!( 1, 98)( 2, 97)( 3,100)( 4, 99)( 5,102)( 6,101)( 7,104)
( 8,103)( 9,106)( 10,105)( 11,108)( 12,107)( 13,110)( 14,109)( 15,112)
( 16,111)( 17,114)( 18,113)( 19,116)( 20,115)( 21,118)( 22,117)( 23,120)
( 24,119)( 25,122)( 26,121)( 27,124)( 28,123)( 29,126)( 30,125)( 31,128)
( 32,127)( 33,130)( 34,129)( 35,132)( 36,131)( 37,134)( 38,133)( 39,136)
( 40,135)( 41,138)( 42,137)( 43,140)( 44,139)( 45,142)( 46,141)( 47,144)
( 48,143)( 49,170)( 50,169)( 51,172)( 52,171)( 53,174)( 54,173)( 55,176)
( 56,175)( 57,178)( 58,177)( 59,180)( 60,179)( 61,182)( 62,181)( 63,184)
( 64,183)( 65,186)( 66,185)( 67,188)( 68,187)( 69,190)( 70,189)( 71,192)
( 72,191)( 73,146)( 74,145)( 75,148)( 76,147)( 77,150)( 78,149)( 79,152)
( 80,151)( 81,154)( 82,153)( 83,156)( 84,155)( 85,158)( 86,157)( 87,160)
( 88,159)( 89,162)( 90,161)( 91,164)( 92,163)( 93,166)( 94,165)( 95,168)
( 96,167)(193,290)(194,289)(195,292)(196,291)(197,294)(198,293)(199,296)
(200,295)(201,298)(202,297)(203,300)(204,299)(205,302)(206,301)(207,304)
(208,303)(209,306)(210,305)(211,308)(212,307)(213,310)(214,309)(215,312)
(216,311)(217,314)(218,313)(219,316)(220,315)(221,318)(222,317)(223,320)
(224,319)(225,322)(226,321)(227,324)(228,323)(229,326)(230,325)(231,328)
(232,327)(233,330)(234,329)(235,332)(236,331)(237,334)(238,333)(239,336)
(240,335)(241,362)(242,361)(243,364)(244,363)(245,366)(246,365)(247,368)
(248,367)(249,370)(250,369)(251,372)(252,371)(253,374)(254,373)(255,376)
(256,375)(257,378)(258,377)(259,380)(260,379)(261,382)(262,381)(263,384)
(264,383)(265,338)(266,337)(267,340)(268,339)(269,342)(270,341)(271,344)
(272,343)(273,346)(274,345)(275,348)(276,347)(277,350)(278,349)(279,352)
(280,351)(281,354)(282,353)(283,356)(284,355)(285,358)(286,357)(287,360)
(288,359);
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope