Polytope of Type {4,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,6}*768b
if this polytope has a name.
Group : SmallGroup(768,1089251)
Rank : 4
Schlafli Type : {4,12,6}
Number of vertices, edges, etc : 4, 32, 48, 8
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 : {4,12,3}*384, {4,6,6}*384, {2,12,6}*384b
4-fold quotients : {4,6,3}*192, {2,12,3}*192, {2,6,6}*192
8-fold quotients : {2,3,6}*96, {2,6,3}*96
16-fold quotients : {2,3,3}*48
24-fold quotients : {4,2,2}*32
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, 50)( 2, 49)( 3, 51)( 4, 52)( 5, 56)( 6, 55)( 7, 54)( 8, 53)
( 9, 66)( 10, 65)( 11, 67)( 12, 68)( 13, 72)( 14, 71)( 15, 70)( 16, 69)
( 17, 58)( 18, 57)( 19, 59)( 20, 60)( 21, 64)( 22, 63)( 23, 62)( 24, 61)
( 25, 74)( 26, 73)( 27, 75)( 28, 76)( 29, 80)( 30, 79)( 31, 78)( 32, 77)
( 33, 90)( 34, 89)( 35, 91)( 36, 92)( 37, 96)( 38, 95)( 39, 94)( 40, 93)
( 41, 82)( 42, 81)( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)( 48, 85)
( 97,146)( 98,145)( 99,147)(100,148)(101,152)(102,151)(103,150)(104,149)
(105,162)(106,161)(107,163)(108,164)(109,168)(110,167)(111,166)(112,165)
(113,154)(114,153)(115,155)(116,156)(117,160)(118,159)(119,158)(120,157)
(121,170)(122,169)(123,171)(124,172)(125,176)(126,175)(127,174)(128,173)
(129,186)(130,185)(131,187)(132,188)(133,192)(134,191)(135,190)(136,189)
(137,178)(138,177)(139,179)(140,180)(141,184)(142,183)(143,182)(144,181)
(193,242)(194,241)(195,243)(196,244)(197,248)(198,247)(199,246)(200,245)
(201,258)(202,257)(203,259)(204,260)(205,264)(206,263)(207,262)(208,261)
(209,250)(210,249)(211,251)(212,252)(213,256)(214,255)(215,254)(216,253)
(217,266)(218,265)(219,267)(220,268)(221,272)(222,271)(223,270)(224,269)
(225,282)(226,281)(227,283)(228,284)(229,288)(230,287)(231,286)(232,285)
(233,274)(234,273)(235,275)(236,276)(237,280)(238,279)(239,278)(240,277)
(289,338)(290,337)(291,339)(292,340)(293,344)(294,343)(295,342)(296,341)
(297,354)(298,353)(299,355)(300,356)(301,360)(302,359)(303,358)(304,357)
(305,346)(306,345)(307,347)(308,348)(309,352)(310,351)(311,350)(312,349)
(313,362)(314,361)(315,363)(316,364)(317,368)(318,367)(319,366)(320,365)
(321,378)(322,377)(323,379)(324,380)(325,384)(326,383)(327,382)(328,381)
(329,370)(330,369)(331,371)(332,372)(333,376)(334,375)(335,374)(336,373);;
s2 := ( 1, 17)( 2, 18)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 24)( 8, 23)
( 11, 14)( 12, 13)( 15, 16)( 25, 41)( 26, 42)( 27, 46)( 28, 45)( 29, 44)
( 30, 43)( 31, 48)( 32, 47)( 35, 38)( 36, 37)( 39, 40)( 49, 66)( 50, 65)
( 51, 69)( 52, 70)( 53, 67)( 54, 68)( 55, 71)( 56, 72)( 57, 58)( 59, 61)
( 60, 62)( 73, 90)( 74, 89)( 75, 93)( 76, 94)( 77, 91)( 78, 92)( 79, 95)
( 80, 96)( 81, 82)( 83, 85)( 84, 86)( 97,113)( 98,114)( 99,118)(100,117)
(101,116)(102,115)(103,120)(104,119)(107,110)(108,109)(111,112)(121,137)
(122,138)(123,142)(124,141)(125,140)(126,139)(127,144)(128,143)(131,134)
(132,133)(135,136)(145,162)(146,161)(147,165)(148,166)(149,163)(150,164)
(151,167)(152,168)(153,154)(155,157)(156,158)(169,186)(170,185)(171,189)
(172,190)(173,187)(174,188)(175,191)(176,192)(177,178)(179,181)(180,182)
(193,209)(194,210)(195,214)(196,213)(197,212)(198,211)(199,216)(200,215)
(203,206)(204,205)(207,208)(217,233)(218,234)(219,238)(220,237)(221,236)
(222,235)(223,240)(224,239)(227,230)(228,229)(231,232)(241,258)(242,257)
(243,261)(244,262)(245,259)(246,260)(247,263)(248,264)(249,250)(251,253)
(252,254)(265,282)(266,281)(267,285)(268,286)(269,283)(270,284)(271,287)
(272,288)(273,274)(275,277)(276,278)(289,305)(290,306)(291,310)(292,309)
(293,308)(294,307)(295,312)(296,311)(299,302)(300,301)(303,304)(313,329)
(314,330)(315,334)(316,333)(317,332)(318,331)(319,336)(320,335)(323,326)
(324,325)(327,328)(337,354)(338,353)(339,357)(340,358)(341,355)(342,356)
(343,359)(344,360)(345,346)(347,349)(348,350)(361,378)(362,377)(363,381)
(364,382)(365,379)(366,380)(367,383)(368,384)(369,370)(371,373)(372,374);;
s3 := ( 1,196)( 2,195)( 3,194)( 4,193)( 5,197)( 6,198)( 7,200)( 8,199)
( 9,212)( 10,211)( 11,210)( 12,209)( 13,213)( 14,214)( 15,216)( 16,215)
( 17,204)( 18,203)( 19,202)( 20,201)( 21,205)( 22,206)( 23,208)( 24,207)
( 25,220)( 26,219)( 27,218)( 28,217)( 29,221)( 30,222)( 31,224)( 32,223)
( 33,236)( 34,235)( 35,234)( 36,233)( 37,237)( 38,238)( 39,240)( 40,239)
( 41,228)( 42,227)( 43,226)( 44,225)( 45,229)( 46,230)( 47,232)( 48,231)
( 49,243)( 50,244)( 51,241)( 52,242)( 53,246)( 54,245)( 55,247)( 56,248)
( 57,259)( 58,260)( 59,257)( 60,258)( 61,262)( 62,261)( 63,263)( 64,264)
( 65,251)( 66,252)( 67,249)( 68,250)( 69,254)( 70,253)( 71,255)( 72,256)
( 73,267)( 74,268)( 75,265)( 76,266)( 77,270)( 78,269)( 79,271)( 80,272)
( 81,283)( 82,284)( 83,281)( 84,282)( 85,286)( 86,285)( 87,287)( 88,288)
( 89,275)( 90,276)( 91,273)( 92,274)( 93,278)( 94,277)( 95,279)( 96,280)
( 97,292)( 98,291)( 99,290)(100,289)(101,293)(102,294)(103,296)(104,295)
(105,308)(106,307)(107,306)(108,305)(109,309)(110,310)(111,312)(112,311)
(113,300)(114,299)(115,298)(116,297)(117,301)(118,302)(119,304)(120,303)
(121,316)(122,315)(123,314)(124,313)(125,317)(126,318)(127,320)(128,319)
(129,332)(130,331)(131,330)(132,329)(133,333)(134,334)(135,336)(136,335)
(137,324)(138,323)(139,322)(140,321)(141,325)(142,326)(143,328)(144,327)
(145,339)(146,340)(147,337)(148,338)(149,342)(150,341)(151,343)(152,344)
(153,355)(154,356)(155,353)(156,354)(157,358)(158,357)(159,359)(160,360)
(161,347)(162,348)(163,345)(164,346)(165,350)(166,349)(167,351)(168,352)
(169,363)(170,364)(171,361)(172,362)(173,366)(174,365)(175,367)(176,368)
(177,379)(178,380)(179,377)(180,378)(181,382)(182,381)(183,383)(184,384)
(185,371)(186,372)(187,369)(188,370)(189,374)(190,373)(191,375)(192,376);;
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, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s1*s2*s3*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, 50)( 2, 49)( 3, 51)( 4, 52)( 5, 56)( 6, 55)( 7, 54)
( 8, 53)( 9, 66)( 10, 65)( 11, 67)( 12, 68)( 13, 72)( 14, 71)( 15, 70)
( 16, 69)( 17, 58)( 18, 57)( 19, 59)( 20, 60)( 21, 64)( 22, 63)( 23, 62)
( 24, 61)( 25, 74)( 26, 73)( 27, 75)( 28, 76)( 29, 80)( 30, 79)( 31, 78)
( 32, 77)( 33, 90)( 34, 89)( 35, 91)( 36, 92)( 37, 96)( 38, 95)( 39, 94)
( 40, 93)( 41, 82)( 42, 81)( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)
( 48, 85)( 97,146)( 98,145)( 99,147)(100,148)(101,152)(102,151)(103,150)
(104,149)(105,162)(106,161)(107,163)(108,164)(109,168)(110,167)(111,166)
(112,165)(113,154)(114,153)(115,155)(116,156)(117,160)(118,159)(119,158)
(120,157)(121,170)(122,169)(123,171)(124,172)(125,176)(126,175)(127,174)
(128,173)(129,186)(130,185)(131,187)(132,188)(133,192)(134,191)(135,190)
(136,189)(137,178)(138,177)(139,179)(140,180)(141,184)(142,183)(143,182)
(144,181)(193,242)(194,241)(195,243)(196,244)(197,248)(198,247)(199,246)
(200,245)(201,258)(202,257)(203,259)(204,260)(205,264)(206,263)(207,262)
(208,261)(209,250)(210,249)(211,251)(212,252)(213,256)(214,255)(215,254)
(216,253)(217,266)(218,265)(219,267)(220,268)(221,272)(222,271)(223,270)
(224,269)(225,282)(226,281)(227,283)(228,284)(229,288)(230,287)(231,286)
(232,285)(233,274)(234,273)(235,275)(236,276)(237,280)(238,279)(239,278)
(240,277)(289,338)(290,337)(291,339)(292,340)(293,344)(294,343)(295,342)
(296,341)(297,354)(298,353)(299,355)(300,356)(301,360)(302,359)(303,358)
(304,357)(305,346)(306,345)(307,347)(308,348)(309,352)(310,351)(311,350)
(312,349)(313,362)(314,361)(315,363)(316,364)(317,368)(318,367)(319,366)
(320,365)(321,378)(322,377)(323,379)(324,380)(325,384)(326,383)(327,382)
(328,381)(329,370)(330,369)(331,371)(332,372)(333,376)(334,375)(335,374)
(336,373);
s2 := Sym(384)!( 1, 17)( 2, 18)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 24)
( 8, 23)( 11, 14)( 12, 13)( 15, 16)( 25, 41)( 26, 42)( 27, 46)( 28, 45)
( 29, 44)( 30, 43)( 31, 48)( 32, 47)( 35, 38)( 36, 37)( 39, 40)( 49, 66)
( 50, 65)( 51, 69)( 52, 70)( 53, 67)( 54, 68)( 55, 71)( 56, 72)( 57, 58)
( 59, 61)( 60, 62)( 73, 90)( 74, 89)( 75, 93)( 76, 94)( 77, 91)( 78, 92)
( 79, 95)( 80, 96)( 81, 82)( 83, 85)( 84, 86)( 97,113)( 98,114)( 99,118)
(100,117)(101,116)(102,115)(103,120)(104,119)(107,110)(108,109)(111,112)
(121,137)(122,138)(123,142)(124,141)(125,140)(126,139)(127,144)(128,143)
(131,134)(132,133)(135,136)(145,162)(146,161)(147,165)(148,166)(149,163)
(150,164)(151,167)(152,168)(153,154)(155,157)(156,158)(169,186)(170,185)
(171,189)(172,190)(173,187)(174,188)(175,191)(176,192)(177,178)(179,181)
(180,182)(193,209)(194,210)(195,214)(196,213)(197,212)(198,211)(199,216)
(200,215)(203,206)(204,205)(207,208)(217,233)(218,234)(219,238)(220,237)
(221,236)(222,235)(223,240)(224,239)(227,230)(228,229)(231,232)(241,258)
(242,257)(243,261)(244,262)(245,259)(246,260)(247,263)(248,264)(249,250)
(251,253)(252,254)(265,282)(266,281)(267,285)(268,286)(269,283)(270,284)
(271,287)(272,288)(273,274)(275,277)(276,278)(289,305)(290,306)(291,310)
(292,309)(293,308)(294,307)(295,312)(296,311)(299,302)(300,301)(303,304)
(313,329)(314,330)(315,334)(316,333)(317,332)(318,331)(319,336)(320,335)
(323,326)(324,325)(327,328)(337,354)(338,353)(339,357)(340,358)(341,355)
(342,356)(343,359)(344,360)(345,346)(347,349)(348,350)(361,378)(362,377)
(363,381)(364,382)(365,379)(366,380)(367,383)(368,384)(369,370)(371,373)
(372,374);
s3 := Sym(384)!( 1,196)( 2,195)( 3,194)( 4,193)( 5,197)( 6,198)( 7,200)
( 8,199)( 9,212)( 10,211)( 11,210)( 12,209)( 13,213)( 14,214)( 15,216)
( 16,215)( 17,204)( 18,203)( 19,202)( 20,201)( 21,205)( 22,206)( 23,208)
( 24,207)( 25,220)( 26,219)( 27,218)( 28,217)( 29,221)( 30,222)( 31,224)
( 32,223)( 33,236)( 34,235)( 35,234)( 36,233)( 37,237)( 38,238)( 39,240)
( 40,239)( 41,228)( 42,227)( 43,226)( 44,225)( 45,229)( 46,230)( 47,232)
( 48,231)( 49,243)( 50,244)( 51,241)( 52,242)( 53,246)( 54,245)( 55,247)
( 56,248)( 57,259)( 58,260)( 59,257)( 60,258)( 61,262)( 62,261)( 63,263)
( 64,264)( 65,251)( 66,252)( 67,249)( 68,250)( 69,254)( 70,253)( 71,255)
( 72,256)( 73,267)( 74,268)( 75,265)( 76,266)( 77,270)( 78,269)( 79,271)
( 80,272)( 81,283)( 82,284)( 83,281)( 84,282)( 85,286)( 86,285)( 87,287)
( 88,288)( 89,275)( 90,276)( 91,273)( 92,274)( 93,278)( 94,277)( 95,279)
( 96,280)( 97,292)( 98,291)( 99,290)(100,289)(101,293)(102,294)(103,296)
(104,295)(105,308)(106,307)(107,306)(108,305)(109,309)(110,310)(111,312)
(112,311)(113,300)(114,299)(115,298)(116,297)(117,301)(118,302)(119,304)
(120,303)(121,316)(122,315)(123,314)(124,313)(125,317)(126,318)(127,320)
(128,319)(129,332)(130,331)(131,330)(132,329)(133,333)(134,334)(135,336)
(136,335)(137,324)(138,323)(139,322)(140,321)(141,325)(142,326)(143,328)
(144,327)(145,339)(146,340)(147,337)(148,338)(149,342)(150,341)(151,343)
(152,344)(153,355)(154,356)(155,353)(156,354)(157,358)(158,357)(159,359)
(160,360)(161,347)(162,348)(163,345)(164,346)(165,350)(166,349)(167,351)
(168,352)(169,363)(170,364)(171,361)(172,362)(173,366)(174,365)(175,367)
(176,368)(177,379)(178,380)(179,377)(180,378)(181,382)(182,381)(183,383)
(184,384)(185,371)(186,372)(187,369)(188,370)(189,374)(190,373)(191,375)
(192,376);
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,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope