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