Polytope of Type {4,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,4}*768e
if this polytope has a name.
Group : SmallGroup(768,1088705)
Rank : 4
Schlafli Type : {4,12,4}
Number of vertices, edges, etc : 4, 48, 48, 8
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 : {4,12,4}*384b, {4,12,4}*384c, {2,12,4}*384b, {4,6,4}*384a
4-fold quotients : {4,12,2}*192a, {2,12,4}*192b, {2,12,4}*192c, {4,6,4}*192b, {2,6,4}*192
8-fold quotients : {2,12,2}*96, {4,6,2}*96a, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
12-fold quotients : {4,4,2}*64
16-fold quotients : {2,3,4}*48, {2,6,2}*48
24-fold quotients : {2,4,2}*32, {4,2,2}*32
32-fold quotients : {2,3,2}*24
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, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)
( 9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)( 16,112)
( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)( 24,120)
( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)
( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)( 48,144)
( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)
( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)
( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)
( 73,145)( 74,146)( 75,147)( 76,148)( 77,149)( 78,150)( 79,151)( 80,152)
( 81,153)( 82,154)( 83,155)( 84,156)( 85,157)( 86,158)( 87,159)( 88,160)
( 89,161)( 90,162)( 91,163)( 92,164)( 93,165)( 94,166)( 95,167)( 96,168)
(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)(200,296)
(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)(208,304)
(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)(216,312)
(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)(224,320)
(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)(232,328)
(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)(240,336)
(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)
(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)(256,376)
(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)
(265,337)(266,338)(267,339)(268,340)(269,341)(270,342)(271,343)(272,344)
(273,345)(274,346)(275,347)(276,348)(277,349)(278,350)(279,351)(280,352)
(281,353)(282,354)(283,355)(284,356)(285,357)(286,358)(287,359)(288,360);;
s1 := ( 1, 61)( 2, 62)( 3, 64)( 4, 63)( 5, 69)( 6, 70)( 7, 72)( 8, 71)
( 9, 65)( 10, 66)( 11, 68)( 12, 67)( 13, 49)( 14, 50)( 15, 52)( 16, 51)
( 17, 57)( 18, 58)( 19, 60)( 20, 59)( 21, 53)( 22, 54)( 23, 56)( 24, 55)
( 25, 85)( 26, 86)( 27, 88)( 28, 87)( 29, 93)( 30, 94)( 31, 96)( 32, 95)
( 33, 89)( 34, 90)( 35, 92)( 36, 91)( 37, 73)( 38, 74)( 39, 76)( 40, 75)
( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 77)( 46, 78)( 47, 80)( 48, 79)
( 97,157)( 98,158)( 99,160)(100,159)(101,165)(102,166)(103,168)(104,167)
(105,161)(106,162)(107,164)(108,163)(109,145)(110,146)(111,148)(112,147)
(113,153)(114,154)(115,156)(116,155)(117,149)(118,150)(119,152)(120,151)
(121,181)(122,182)(123,184)(124,183)(125,189)(126,190)(127,192)(128,191)
(129,185)(130,186)(131,188)(132,187)(133,169)(134,170)(135,172)(136,171)
(137,177)(138,178)(139,180)(140,179)(141,173)(142,174)(143,176)(144,175)
(193,253)(194,254)(195,256)(196,255)(197,261)(198,262)(199,264)(200,263)
(201,257)(202,258)(203,260)(204,259)(205,241)(206,242)(207,244)(208,243)
(209,249)(210,250)(211,252)(212,251)(213,245)(214,246)(215,248)(216,247)
(217,277)(218,278)(219,280)(220,279)(221,285)(222,286)(223,288)(224,287)
(225,281)(226,282)(227,284)(228,283)(229,265)(230,266)(231,268)(232,267)
(233,273)(234,274)(235,276)(236,275)(237,269)(238,270)(239,272)(240,271)
(289,349)(290,350)(291,352)(292,351)(293,357)(294,358)(295,360)(296,359)
(297,353)(298,354)(299,356)(300,355)(301,337)(302,338)(303,340)(304,339)
(305,345)(306,346)(307,348)(308,347)(309,341)(310,342)(311,344)(312,343)
(313,373)(314,374)(315,376)(316,375)(317,381)(318,382)(319,384)(320,383)
(321,377)(322,378)(323,380)(324,379)(325,361)(326,362)(327,364)(328,363)
(329,369)(330,370)(331,372)(332,371)(333,365)(334,366)(335,368)(336,367);;
s2 := ( 1, 9)( 2, 11)( 3, 10)( 4, 12)( 6, 7)( 13, 21)( 14, 23)( 15, 22)
( 16, 24)( 18, 19)( 25, 33)( 26, 35)( 27, 34)( 28, 36)( 30, 31)( 37, 45)
( 38, 47)( 39, 46)( 40, 48)( 42, 43)( 49, 69)( 50, 71)( 51, 70)( 52, 72)
( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 61)( 58, 63)( 59, 62)( 60, 64)
( 73, 93)( 74, 95)( 75, 94)( 76, 96)( 77, 89)( 78, 91)( 79, 90)( 80, 92)
( 81, 85)( 82, 87)( 83, 86)( 84, 88)( 97,105)( 98,107)( 99,106)(100,108)
(102,103)(109,117)(110,119)(111,118)(112,120)(114,115)(121,129)(122,131)
(123,130)(124,132)(126,127)(133,141)(134,143)(135,142)(136,144)(138,139)
(145,165)(146,167)(147,166)(148,168)(149,161)(150,163)(151,162)(152,164)
(153,157)(154,159)(155,158)(156,160)(169,189)(170,191)(171,190)(172,192)
(173,185)(174,187)(175,186)(176,188)(177,181)(178,183)(179,182)(180,184)
(193,201)(194,203)(195,202)(196,204)(198,199)(205,213)(206,215)(207,214)
(208,216)(210,211)(217,225)(218,227)(219,226)(220,228)(222,223)(229,237)
(230,239)(231,238)(232,240)(234,235)(241,261)(242,263)(243,262)(244,264)
(245,257)(246,259)(247,258)(248,260)(249,253)(250,255)(251,254)(252,256)
(265,285)(266,287)(267,286)(268,288)(269,281)(270,283)(271,282)(272,284)
(273,277)(274,279)(275,278)(276,280)(289,297)(290,299)(291,298)(292,300)
(294,295)(301,309)(302,311)(303,310)(304,312)(306,307)(313,321)(314,323)
(315,322)(316,324)(318,319)(325,333)(326,335)(327,334)(328,336)(330,331)
(337,357)(338,359)(339,358)(340,360)(341,353)(342,355)(343,354)(344,356)
(345,349)(346,351)(347,350)(348,352)(361,381)(362,383)(363,382)(364,384)
(365,377)(366,379)(367,378)(368,380)(369,373)(370,375)(371,374)(372,376);;
s3 := ( 1,194)( 2,193)( 3,196)( 4,195)( 5,198)( 6,197)( 7,200)( 8,199)
( 9,202)( 10,201)( 11,204)( 12,203)( 13,206)( 14,205)( 15,208)( 16,207)
( 17,210)( 18,209)( 19,212)( 20,211)( 21,214)( 22,213)( 23,216)( 24,215)
( 25,218)( 26,217)( 27,220)( 28,219)( 29,222)( 30,221)( 31,224)( 32,223)
( 33,226)( 34,225)( 35,228)( 36,227)( 37,230)( 38,229)( 39,232)( 40,231)
( 41,234)( 42,233)( 43,236)( 44,235)( 45,238)( 46,237)( 47,240)( 48,239)
( 49,242)( 50,241)( 51,244)( 52,243)( 53,246)( 54,245)( 55,248)( 56,247)
( 57,250)( 58,249)( 59,252)( 60,251)( 61,254)( 62,253)( 63,256)( 64,255)
( 65,258)( 66,257)( 67,260)( 68,259)( 69,262)( 70,261)( 71,264)( 72,263)
( 73,266)( 74,265)( 75,268)( 76,267)( 77,270)( 78,269)( 79,272)( 80,271)
( 81,274)( 82,273)( 83,276)( 84,275)( 85,278)( 86,277)( 87,280)( 88,279)
( 89,282)( 90,281)( 91,284)( 92,283)( 93,286)( 94,285)( 95,288)( 96,287)
( 97,290)( 98,289)( 99,292)(100,291)(101,294)(102,293)(103,296)(104,295)
(105,298)(106,297)(107,300)(108,299)(109,302)(110,301)(111,304)(112,303)
(113,306)(114,305)(115,308)(116,307)(117,310)(118,309)(119,312)(120,311)
(121,314)(122,313)(123,316)(124,315)(125,318)(126,317)(127,320)(128,319)
(129,322)(130,321)(131,324)(132,323)(133,326)(134,325)(135,328)(136,327)
(137,330)(138,329)(139,332)(140,331)(141,334)(142,333)(143,336)(144,335)
(145,338)(146,337)(147,340)(148,339)(149,342)(150,341)(151,344)(152,343)
(153,346)(154,345)(155,348)(156,347)(157,350)(158,349)(159,352)(160,351)
(161,354)(162,353)(163,356)(164,355)(165,358)(166,357)(167,360)(168,359)
(169,362)(170,361)(171,364)(172,363)(173,366)(174,365)(175,368)(176,367)
(177,370)(178,369)(179,372)(180,371)(181,374)(182,373)(183,376)(184,375)
(185,378)(186,377)(187,380)(188,379)(189,382)(190,381)(191,384)(192,383);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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, 99)( 4,100)( 5,101)( 6,102)( 7,103)
( 8,104)( 9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)
( 16,112)( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)
( 24,120)( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)
( 32,128)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)
( 40,136)( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)
( 48,144)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)
( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)
( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)
( 72,192)( 73,145)( 74,146)( 75,147)( 76,148)( 77,149)( 78,150)( 79,151)
( 80,152)( 81,153)( 82,154)( 83,155)( 84,156)( 85,157)( 86,158)( 87,159)
( 88,160)( 89,161)( 90,162)( 91,163)( 92,164)( 93,165)( 94,166)( 95,167)
( 96,168)(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)
(200,296)(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)
(208,304)(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)
(216,312)(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)
(224,320)(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)
(232,328)(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)
(240,336)(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)
(248,368)(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)
(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)
(264,384)(265,337)(266,338)(267,339)(268,340)(269,341)(270,342)(271,343)
(272,344)(273,345)(274,346)(275,347)(276,348)(277,349)(278,350)(279,351)
(280,352)(281,353)(282,354)(283,355)(284,356)(285,357)(286,358)(287,359)
(288,360);
s1 := Sym(384)!( 1, 61)( 2, 62)( 3, 64)( 4, 63)( 5, 69)( 6, 70)( 7, 72)
( 8, 71)( 9, 65)( 10, 66)( 11, 68)( 12, 67)( 13, 49)( 14, 50)( 15, 52)
( 16, 51)( 17, 57)( 18, 58)( 19, 60)( 20, 59)( 21, 53)( 22, 54)( 23, 56)
( 24, 55)( 25, 85)( 26, 86)( 27, 88)( 28, 87)( 29, 93)( 30, 94)( 31, 96)
( 32, 95)( 33, 89)( 34, 90)( 35, 92)( 36, 91)( 37, 73)( 38, 74)( 39, 76)
( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 77)( 46, 78)( 47, 80)
( 48, 79)( 97,157)( 98,158)( 99,160)(100,159)(101,165)(102,166)(103,168)
(104,167)(105,161)(106,162)(107,164)(108,163)(109,145)(110,146)(111,148)
(112,147)(113,153)(114,154)(115,156)(116,155)(117,149)(118,150)(119,152)
(120,151)(121,181)(122,182)(123,184)(124,183)(125,189)(126,190)(127,192)
(128,191)(129,185)(130,186)(131,188)(132,187)(133,169)(134,170)(135,172)
(136,171)(137,177)(138,178)(139,180)(140,179)(141,173)(142,174)(143,176)
(144,175)(193,253)(194,254)(195,256)(196,255)(197,261)(198,262)(199,264)
(200,263)(201,257)(202,258)(203,260)(204,259)(205,241)(206,242)(207,244)
(208,243)(209,249)(210,250)(211,252)(212,251)(213,245)(214,246)(215,248)
(216,247)(217,277)(218,278)(219,280)(220,279)(221,285)(222,286)(223,288)
(224,287)(225,281)(226,282)(227,284)(228,283)(229,265)(230,266)(231,268)
(232,267)(233,273)(234,274)(235,276)(236,275)(237,269)(238,270)(239,272)
(240,271)(289,349)(290,350)(291,352)(292,351)(293,357)(294,358)(295,360)
(296,359)(297,353)(298,354)(299,356)(300,355)(301,337)(302,338)(303,340)
(304,339)(305,345)(306,346)(307,348)(308,347)(309,341)(310,342)(311,344)
(312,343)(313,373)(314,374)(315,376)(316,375)(317,381)(318,382)(319,384)
(320,383)(321,377)(322,378)(323,380)(324,379)(325,361)(326,362)(327,364)
(328,363)(329,369)(330,370)(331,372)(332,371)(333,365)(334,366)(335,368)
(336,367);
s2 := Sym(384)!( 1, 9)( 2, 11)( 3, 10)( 4, 12)( 6, 7)( 13, 21)( 14, 23)
( 15, 22)( 16, 24)( 18, 19)( 25, 33)( 26, 35)( 27, 34)( 28, 36)( 30, 31)
( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 42, 43)( 49, 69)( 50, 71)( 51, 70)
( 52, 72)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 61)( 58, 63)( 59, 62)
( 60, 64)( 73, 93)( 74, 95)( 75, 94)( 76, 96)( 77, 89)( 78, 91)( 79, 90)
( 80, 92)( 81, 85)( 82, 87)( 83, 86)( 84, 88)( 97,105)( 98,107)( 99,106)
(100,108)(102,103)(109,117)(110,119)(111,118)(112,120)(114,115)(121,129)
(122,131)(123,130)(124,132)(126,127)(133,141)(134,143)(135,142)(136,144)
(138,139)(145,165)(146,167)(147,166)(148,168)(149,161)(150,163)(151,162)
(152,164)(153,157)(154,159)(155,158)(156,160)(169,189)(170,191)(171,190)
(172,192)(173,185)(174,187)(175,186)(176,188)(177,181)(178,183)(179,182)
(180,184)(193,201)(194,203)(195,202)(196,204)(198,199)(205,213)(206,215)
(207,214)(208,216)(210,211)(217,225)(218,227)(219,226)(220,228)(222,223)
(229,237)(230,239)(231,238)(232,240)(234,235)(241,261)(242,263)(243,262)
(244,264)(245,257)(246,259)(247,258)(248,260)(249,253)(250,255)(251,254)
(252,256)(265,285)(266,287)(267,286)(268,288)(269,281)(270,283)(271,282)
(272,284)(273,277)(274,279)(275,278)(276,280)(289,297)(290,299)(291,298)
(292,300)(294,295)(301,309)(302,311)(303,310)(304,312)(306,307)(313,321)
(314,323)(315,322)(316,324)(318,319)(325,333)(326,335)(327,334)(328,336)
(330,331)(337,357)(338,359)(339,358)(340,360)(341,353)(342,355)(343,354)
(344,356)(345,349)(346,351)(347,350)(348,352)(361,381)(362,383)(363,382)
(364,384)(365,377)(366,379)(367,378)(368,380)(369,373)(370,375)(371,374)
(372,376);
s3 := Sym(384)!( 1,194)( 2,193)( 3,196)( 4,195)( 5,198)( 6,197)( 7,200)
( 8,199)( 9,202)( 10,201)( 11,204)( 12,203)( 13,206)( 14,205)( 15,208)
( 16,207)( 17,210)( 18,209)( 19,212)( 20,211)( 21,214)( 22,213)( 23,216)
( 24,215)( 25,218)( 26,217)( 27,220)( 28,219)( 29,222)( 30,221)( 31,224)
( 32,223)( 33,226)( 34,225)( 35,228)( 36,227)( 37,230)( 38,229)( 39,232)
( 40,231)( 41,234)( 42,233)( 43,236)( 44,235)( 45,238)( 46,237)( 47,240)
( 48,239)( 49,242)( 50,241)( 51,244)( 52,243)( 53,246)( 54,245)( 55,248)
( 56,247)( 57,250)( 58,249)( 59,252)( 60,251)( 61,254)( 62,253)( 63,256)
( 64,255)( 65,258)( 66,257)( 67,260)( 68,259)( 69,262)( 70,261)( 71,264)
( 72,263)( 73,266)( 74,265)( 75,268)( 76,267)( 77,270)( 78,269)( 79,272)
( 80,271)( 81,274)( 82,273)( 83,276)( 84,275)( 85,278)( 86,277)( 87,280)
( 88,279)( 89,282)( 90,281)( 91,284)( 92,283)( 93,286)( 94,285)( 95,288)
( 96,287)( 97,290)( 98,289)( 99,292)(100,291)(101,294)(102,293)(103,296)
(104,295)(105,298)(106,297)(107,300)(108,299)(109,302)(110,301)(111,304)
(112,303)(113,306)(114,305)(115,308)(116,307)(117,310)(118,309)(119,312)
(120,311)(121,314)(122,313)(123,316)(124,315)(125,318)(126,317)(127,320)
(128,319)(129,322)(130,321)(131,324)(132,323)(133,326)(134,325)(135,328)
(136,327)(137,330)(138,329)(139,332)(140,331)(141,334)(142,333)(143,336)
(144,335)(145,338)(146,337)(147,340)(148,339)(149,342)(150,341)(151,344)
(152,343)(153,346)(154,345)(155,348)(156,347)(157,350)(158,349)(159,352)
(160,351)(161,354)(162,353)(163,356)(164,355)(165,358)(166,357)(167,360)
(168,359)(169,362)(170,361)(171,364)(172,363)(173,366)(174,365)(175,368)
(176,367)(177,370)(178,369)(179,372)(180,371)(181,374)(182,373)(183,376)
(184,375)(185,378)(186,377)(187,380)(188,379)(189,382)(190,381)(191,384)
(192,383);
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,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope