Polytope of Type {4,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,4}*768n
if this polytope has a name.
Group : SmallGroup(768,1090188)
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 :
Non-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}*384h, {4,12,4}*384i, {4,6,4}*384c
4-fold quotients : {4,12,2}*192c, {4,3,4}*192a, {4,6,4}*192d, {4,6,4}*192e
8-fold quotients : {4,6,2}*96c, {4,3,4}*96
16-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 52)( 2, 51)( 3, 50)( 4, 49)( 5, 56)( 6, 55)( 7, 54)( 8, 53)
( 9, 60)( 10, 59)( 11, 58)( 12, 57)( 13, 64)( 14, 63)( 15, 62)( 16, 61)
( 17, 68)( 18, 67)( 19, 66)( 20, 65)( 21, 72)( 22, 71)( 23, 70)( 24, 69)
( 25, 76)( 26, 75)( 27, 74)( 28, 73)( 29, 80)( 30, 79)( 31, 78)( 32, 77)
( 33, 84)( 34, 83)( 35, 82)( 36, 81)( 37, 88)( 38, 87)( 39, 86)( 40, 85)
( 41, 92)( 42, 91)( 43, 90)( 44, 89)( 45, 96)( 46, 95)( 47, 94)( 48, 93)
( 97,148)( 98,147)( 99,146)(100,145)(101,152)(102,151)(103,150)(104,149)
(105,156)(106,155)(107,154)(108,153)(109,160)(110,159)(111,158)(112,157)
(113,164)(114,163)(115,162)(116,161)(117,168)(118,167)(119,166)(120,165)
(121,172)(122,171)(123,170)(124,169)(125,176)(126,175)(127,174)(128,173)
(129,180)(130,179)(131,178)(132,177)(133,184)(134,183)(135,182)(136,181)
(137,188)(138,187)(139,186)(140,185)(141,192)(142,191)(143,190)(144,189)
(193,244)(194,243)(195,242)(196,241)(197,248)(198,247)(199,246)(200,245)
(201,252)(202,251)(203,250)(204,249)(205,256)(206,255)(207,254)(208,253)
(209,260)(210,259)(211,258)(212,257)(213,264)(214,263)(215,262)(216,261)
(217,268)(218,267)(219,266)(220,265)(221,272)(222,271)(223,270)(224,269)
(225,276)(226,275)(227,274)(228,273)(229,280)(230,279)(231,278)(232,277)
(233,284)(234,283)(235,282)(236,281)(237,288)(238,287)(239,286)(240,285)
(289,340)(290,339)(291,338)(292,337)(293,344)(294,343)(295,342)(296,341)
(297,348)(298,347)(299,346)(300,345)(301,352)(302,351)(303,350)(304,349)
(305,356)(306,355)(307,354)(308,353)(309,360)(310,359)(311,358)(312,357)
(313,364)(314,363)(315,362)(316,361)(317,368)(318,367)(319,366)(320,365)
(321,372)(322,371)(323,370)(324,369)(325,376)(326,375)(327,374)(328,373)
(329,380)(330,379)(331,378)(332,377)(333,384)(334,383)(335,382)(336,381);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)( 55, 56)
( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)( 68, 83)
( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 93)( 74, 94)( 75, 96)( 76, 95)
( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 97,145)( 98,146)( 99,148)(100,147)
(101,149)(102,150)(103,152)(104,151)(105,157)(106,158)(107,160)(108,159)
(109,153)(110,154)(111,156)(112,155)(113,177)(114,178)(115,180)(116,179)
(117,181)(118,182)(119,184)(120,183)(121,189)(122,190)(123,192)(124,191)
(125,185)(126,186)(127,188)(128,187)(129,161)(130,162)(131,164)(132,163)
(133,165)(134,166)(135,168)(136,167)(137,173)(138,174)(139,176)(140,175)
(141,169)(142,170)(143,172)(144,171)(195,196)(199,200)(201,205)(202,206)
(203,208)(204,207)(209,225)(210,226)(211,228)(212,227)(213,229)(214,230)
(215,232)(216,231)(217,237)(218,238)(219,240)(220,239)(221,233)(222,234)
(223,236)(224,235)(243,244)(247,248)(249,253)(250,254)(251,256)(252,255)
(257,273)(258,274)(259,276)(260,275)(261,277)(262,278)(263,280)(264,279)
(265,285)(266,286)(267,288)(268,287)(269,281)(270,282)(271,284)(272,283)
(289,337)(290,338)(291,340)(292,339)(293,341)(294,342)(295,344)(296,343)
(297,349)(298,350)(299,352)(300,351)(301,345)(302,346)(303,348)(304,347)
(305,369)(306,370)(307,372)(308,371)(309,373)(310,374)(311,376)(312,375)
(313,381)(314,382)(315,384)(316,383)(317,377)(318,378)(319,380)(320,379)
(321,353)(322,354)(323,356)(324,355)(325,357)(326,358)(327,360)(328,359)
(329,365)(330,366)(331,368)(332,367)(333,361)(334,362)(335,364)(336,363);;
s2 := ( 1,177)( 2,179)( 3,178)( 4,180)( 5,185)( 6,187)( 7,186)( 8,188)
( 9,181)( 10,183)( 11,182)( 12,184)( 13,189)( 14,191)( 15,190)( 16,192)
( 17,161)( 18,163)( 19,162)( 20,164)( 21,169)( 22,171)( 23,170)( 24,172)
( 25,165)( 26,167)( 27,166)( 28,168)( 29,173)( 30,175)( 31,174)( 32,176)
( 33,145)( 34,147)( 35,146)( 36,148)( 37,153)( 38,155)( 39,154)( 40,156)
( 41,149)( 42,151)( 43,150)( 44,152)( 45,157)( 46,159)( 47,158)( 48,160)
( 49,129)( 50,131)( 51,130)( 52,132)( 53,137)( 54,139)( 55,138)( 56,140)
( 57,133)( 58,135)( 59,134)( 60,136)( 61,141)( 62,143)( 63,142)( 64,144)
( 65,113)( 66,115)( 67,114)( 68,116)( 69,121)( 70,123)( 71,122)( 72,124)
( 73,117)( 74,119)( 75,118)( 76,120)( 77,125)( 78,127)( 79,126)( 80,128)
( 81, 97)( 82, 99)( 83, 98)( 84,100)( 85,105)( 86,107)( 87,106)( 88,108)
( 89,101)( 90,103)( 91,102)( 92,104)( 93,109)( 94,111)( 95,110)( 96,112)
(193,369)(194,371)(195,370)(196,372)(197,377)(198,379)(199,378)(200,380)
(201,373)(202,375)(203,374)(204,376)(205,381)(206,383)(207,382)(208,384)
(209,353)(210,355)(211,354)(212,356)(213,361)(214,363)(215,362)(216,364)
(217,357)(218,359)(219,358)(220,360)(221,365)(222,367)(223,366)(224,368)
(225,337)(226,339)(227,338)(228,340)(229,345)(230,347)(231,346)(232,348)
(233,341)(234,343)(235,342)(236,344)(237,349)(238,351)(239,350)(240,352)
(241,321)(242,323)(243,322)(244,324)(245,329)(246,331)(247,330)(248,332)
(249,325)(250,327)(251,326)(252,328)(253,333)(254,335)(255,334)(256,336)
(257,305)(258,307)(259,306)(260,308)(261,313)(262,315)(263,314)(264,316)
(265,309)(266,311)(267,310)(268,312)(269,317)(270,319)(271,318)(272,320)
(273,289)(274,291)(275,290)(276,292)(277,297)(278,299)(279,298)(280,300)
(281,293)(282,295)(283,294)(284,296)(285,301)(286,303)(287,302)(288,304);;
s3 := ( 1,197)( 2,198)( 3,199)( 4,200)( 5,193)( 6,194)( 7,195)( 8,196)
( 9,205)( 10,206)( 11,207)( 12,208)( 13,201)( 14,202)( 15,203)( 16,204)
( 17,213)( 18,214)( 19,215)( 20,216)( 21,209)( 22,210)( 23,211)( 24,212)
( 25,221)( 26,222)( 27,223)( 28,224)( 29,217)( 30,218)( 31,219)( 32,220)
( 33,229)( 34,230)( 35,231)( 36,232)( 37,225)( 38,226)( 39,227)( 40,228)
( 41,237)( 42,238)( 43,239)( 44,240)( 45,233)( 46,234)( 47,235)( 48,236)
( 49,245)( 50,246)( 51,247)( 52,248)( 53,241)( 54,242)( 55,243)( 56,244)
( 57,253)( 58,254)( 59,255)( 60,256)( 61,249)( 62,250)( 63,251)( 64,252)
( 65,261)( 66,262)( 67,263)( 68,264)( 69,257)( 70,258)( 71,259)( 72,260)
( 73,269)( 74,270)( 75,271)( 76,272)( 77,265)( 78,266)( 79,267)( 80,268)
( 81,277)( 82,278)( 83,279)( 84,280)( 85,273)( 86,274)( 87,275)( 88,276)
( 89,285)( 90,286)( 91,287)( 92,288)( 93,281)( 94,282)( 95,283)( 96,284)
( 97,293)( 98,294)( 99,295)(100,296)(101,289)(102,290)(103,291)(104,292)
(105,301)(106,302)(107,303)(108,304)(109,297)(110,298)(111,299)(112,300)
(113,309)(114,310)(115,311)(116,312)(117,305)(118,306)(119,307)(120,308)
(121,317)(122,318)(123,319)(124,320)(125,313)(126,314)(127,315)(128,316)
(129,325)(130,326)(131,327)(132,328)(133,321)(134,322)(135,323)(136,324)
(137,333)(138,334)(139,335)(140,336)(141,329)(142,330)(143,331)(144,332)
(145,341)(146,342)(147,343)(148,344)(149,337)(150,338)(151,339)(152,340)
(153,349)(154,350)(155,351)(156,352)(157,345)(158,346)(159,347)(160,348)
(161,357)(162,358)(163,359)(164,360)(165,353)(166,354)(167,355)(168,356)
(169,365)(170,366)(171,367)(172,368)(173,361)(174,362)(175,363)(176,364)
(177,373)(178,374)(179,375)(180,376)(181,369)(182,370)(183,371)(184,372)
(185,381)(186,382)(187,383)(188,384)(189,377)(190,378)(191,379)(192,380);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1, 52)( 2, 51)( 3, 50)( 4, 49)( 5, 56)( 6, 55)( 7, 54)
( 8, 53)( 9, 60)( 10, 59)( 11, 58)( 12, 57)( 13, 64)( 14, 63)( 15, 62)
( 16, 61)( 17, 68)( 18, 67)( 19, 66)( 20, 65)( 21, 72)( 22, 71)( 23, 70)
( 24, 69)( 25, 76)( 26, 75)( 27, 74)( 28, 73)( 29, 80)( 30, 79)( 31, 78)
( 32, 77)( 33, 84)( 34, 83)( 35, 82)( 36, 81)( 37, 88)( 38, 87)( 39, 86)
( 40, 85)( 41, 92)( 42, 91)( 43, 90)( 44, 89)( 45, 96)( 46, 95)( 47, 94)
( 48, 93)( 97,148)( 98,147)( 99,146)(100,145)(101,152)(102,151)(103,150)
(104,149)(105,156)(106,155)(107,154)(108,153)(109,160)(110,159)(111,158)
(112,157)(113,164)(114,163)(115,162)(116,161)(117,168)(118,167)(119,166)
(120,165)(121,172)(122,171)(123,170)(124,169)(125,176)(126,175)(127,174)
(128,173)(129,180)(130,179)(131,178)(132,177)(133,184)(134,183)(135,182)
(136,181)(137,188)(138,187)(139,186)(140,185)(141,192)(142,191)(143,190)
(144,189)(193,244)(194,243)(195,242)(196,241)(197,248)(198,247)(199,246)
(200,245)(201,252)(202,251)(203,250)(204,249)(205,256)(206,255)(207,254)
(208,253)(209,260)(210,259)(211,258)(212,257)(213,264)(214,263)(215,262)
(216,261)(217,268)(218,267)(219,266)(220,265)(221,272)(222,271)(223,270)
(224,269)(225,276)(226,275)(227,274)(228,273)(229,280)(230,279)(231,278)
(232,277)(233,284)(234,283)(235,282)(236,281)(237,288)(238,287)(239,286)
(240,285)(289,340)(290,339)(291,338)(292,337)(293,344)(294,343)(295,342)
(296,341)(297,348)(298,347)(299,346)(300,345)(301,352)(302,351)(303,350)
(304,349)(305,356)(306,355)(307,354)(308,353)(309,360)(310,359)(311,358)
(312,357)(313,364)(314,363)(315,362)(316,361)(317,368)(318,367)(319,366)
(320,365)(321,372)(322,371)(323,370)(324,369)(325,376)(326,375)(327,374)
(328,373)(329,380)(330,379)(331,378)(332,377)(333,384)(334,383)(335,382)
(336,381);
s1 := Sym(384)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)
( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)
( 55, 56)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)
( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 93)( 74, 94)( 75, 96)
( 76, 95)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 97,145)( 98,146)( 99,148)
(100,147)(101,149)(102,150)(103,152)(104,151)(105,157)(106,158)(107,160)
(108,159)(109,153)(110,154)(111,156)(112,155)(113,177)(114,178)(115,180)
(116,179)(117,181)(118,182)(119,184)(120,183)(121,189)(122,190)(123,192)
(124,191)(125,185)(126,186)(127,188)(128,187)(129,161)(130,162)(131,164)
(132,163)(133,165)(134,166)(135,168)(136,167)(137,173)(138,174)(139,176)
(140,175)(141,169)(142,170)(143,172)(144,171)(195,196)(199,200)(201,205)
(202,206)(203,208)(204,207)(209,225)(210,226)(211,228)(212,227)(213,229)
(214,230)(215,232)(216,231)(217,237)(218,238)(219,240)(220,239)(221,233)
(222,234)(223,236)(224,235)(243,244)(247,248)(249,253)(250,254)(251,256)
(252,255)(257,273)(258,274)(259,276)(260,275)(261,277)(262,278)(263,280)
(264,279)(265,285)(266,286)(267,288)(268,287)(269,281)(270,282)(271,284)
(272,283)(289,337)(290,338)(291,340)(292,339)(293,341)(294,342)(295,344)
(296,343)(297,349)(298,350)(299,352)(300,351)(301,345)(302,346)(303,348)
(304,347)(305,369)(306,370)(307,372)(308,371)(309,373)(310,374)(311,376)
(312,375)(313,381)(314,382)(315,384)(316,383)(317,377)(318,378)(319,380)
(320,379)(321,353)(322,354)(323,356)(324,355)(325,357)(326,358)(327,360)
(328,359)(329,365)(330,366)(331,368)(332,367)(333,361)(334,362)(335,364)
(336,363);
s2 := Sym(384)!( 1,177)( 2,179)( 3,178)( 4,180)( 5,185)( 6,187)( 7,186)
( 8,188)( 9,181)( 10,183)( 11,182)( 12,184)( 13,189)( 14,191)( 15,190)
( 16,192)( 17,161)( 18,163)( 19,162)( 20,164)( 21,169)( 22,171)( 23,170)
( 24,172)( 25,165)( 26,167)( 27,166)( 28,168)( 29,173)( 30,175)( 31,174)
( 32,176)( 33,145)( 34,147)( 35,146)( 36,148)( 37,153)( 38,155)( 39,154)
( 40,156)( 41,149)( 42,151)( 43,150)( 44,152)( 45,157)( 46,159)( 47,158)
( 48,160)( 49,129)( 50,131)( 51,130)( 52,132)( 53,137)( 54,139)( 55,138)
( 56,140)( 57,133)( 58,135)( 59,134)( 60,136)( 61,141)( 62,143)( 63,142)
( 64,144)( 65,113)( 66,115)( 67,114)( 68,116)( 69,121)( 70,123)( 71,122)
( 72,124)( 73,117)( 74,119)( 75,118)( 76,120)( 77,125)( 78,127)( 79,126)
( 80,128)( 81, 97)( 82, 99)( 83, 98)( 84,100)( 85,105)( 86,107)( 87,106)
( 88,108)( 89,101)( 90,103)( 91,102)( 92,104)( 93,109)( 94,111)( 95,110)
( 96,112)(193,369)(194,371)(195,370)(196,372)(197,377)(198,379)(199,378)
(200,380)(201,373)(202,375)(203,374)(204,376)(205,381)(206,383)(207,382)
(208,384)(209,353)(210,355)(211,354)(212,356)(213,361)(214,363)(215,362)
(216,364)(217,357)(218,359)(219,358)(220,360)(221,365)(222,367)(223,366)
(224,368)(225,337)(226,339)(227,338)(228,340)(229,345)(230,347)(231,346)
(232,348)(233,341)(234,343)(235,342)(236,344)(237,349)(238,351)(239,350)
(240,352)(241,321)(242,323)(243,322)(244,324)(245,329)(246,331)(247,330)
(248,332)(249,325)(250,327)(251,326)(252,328)(253,333)(254,335)(255,334)
(256,336)(257,305)(258,307)(259,306)(260,308)(261,313)(262,315)(263,314)
(264,316)(265,309)(266,311)(267,310)(268,312)(269,317)(270,319)(271,318)
(272,320)(273,289)(274,291)(275,290)(276,292)(277,297)(278,299)(279,298)
(280,300)(281,293)(282,295)(283,294)(284,296)(285,301)(286,303)(287,302)
(288,304);
s3 := Sym(384)!( 1,197)( 2,198)( 3,199)( 4,200)( 5,193)( 6,194)( 7,195)
( 8,196)( 9,205)( 10,206)( 11,207)( 12,208)( 13,201)( 14,202)( 15,203)
( 16,204)( 17,213)( 18,214)( 19,215)( 20,216)( 21,209)( 22,210)( 23,211)
( 24,212)( 25,221)( 26,222)( 27,223)( 28,224)( 29,217)( 30,218)( 31,219)
( 32,220)( 33,229)( 34,230)( 35,231)( 36,232)( 37,225)( 38,226)( 39,227)
( 40,228)( 41,237)( 42,238)( 43,239)( 44,240)( 45,233)( 46,234)( 47,235)
( 48,236)( 49,245)( 50,246)( 51,247)( 52,248)( 53,241)( 54,242)( 55,243)
( 56,244)( 57,253)( 58,254)( 59,255)( 60,256)( 61,249)( 62,250)( 63,251)
( 64,252)( 65,261)( 66,262)( 67,263)( 68,264)( 69,257)( 70,258)( 71,259)
( 72,260)( 73,269)( 74,270)( 75,271)( 76,272)( 77,265)( 78,266)( 79,267)
( 80,268)( 81,277)( 82,278)( 83,279)( 84,280)( 85,273)( 86,274)( 87,275)
( 88,276)( 89,285)( 90,286)( 91,287)( 92,288)( 93,281)( 94,282)( 95,283)
( 96,284)( 97,293)( 98,294)( 99,295)(100,296)(101,289)(102,290)(103,291)
(104,292)(105,301)(106,302)(107,303)(108,304)(109,297)(110,298)(111,299)
(112,300)(113,309)(114,310)(115,311)(116,312)(117,305)(118,306)(119,307)
(120,308)(121,317)(122,318)(123,319)(124,320)(125,313)(126,314)(127,315)
(128,316)(129,325)(130,326)(131,327)(132,328)(133,321)(134,322)(135,323)
(136,324)(137,333)(138,334)(139,335)(140,336)(141,329)(142,330)(143,331)
(144,332)(145,341)(146,342)(147,343)(148,344)(149,337)(150,338)(151,339)
(152,340)(153,349)(154,350)(155,351)(156,352)(157,345)(158,346)(159,347)
(160,348)(161,357)(162,358)(163,359)(164,360)(165,353)(166,354)(167,355)
(168,356)(169,365)(170,366)(171,367)(172,368)(173,361)(174,362)(175,363)
(176,364)(177,373)(178,374)(179,375)(180,376)(181,369)(182,370)(183,371)
(184,372)(185,381)(186,382)(187,383)(188,384)(189,377)(190,378)(191,379)
(192,380);
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, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 >;
References : None.
to this polytope