Polytope of Type {12,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,8}*768b
if this polytope has a name.
Group : SmallGroup(768,200904)
Rank : 4
Schlafli Type : {12,4,8}
Number of vertices, edges, etc : 12, 24, 16, 8
Order of s0s1s2s3 : 24
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 : {12,4,4}*384, {6,4,8}*384b
3-fold quotients : {4,4,8}*256b
4-fold quotients : {12,4,2}*192a, {12,2,4}*192, {6,4,4}*192
6-fold quotients : {4,4,4}*128, {2,4,8}*128b
8-fold quotients : {12,2,2}*96, {6,2,4}*96, {6,4,2}*96a
12-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
16-fold quotients : {3,2,4}*48, {6,2,2}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*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 := ( 1,241)( 2,243)( 3,242)( 4,244)( 5,246)( 6,245)( 7,247)( 8,249)
( 9,248)( 10,250)( 11,252)( 12,251)( 13,253)( 14,255)( 15,254)( 16,256)
( 17,258)( 18,257)( 19,259)( 20,261)( 21,260)( 22,262)( 23,264)( 24,263)
( 25,265)( 26,267)( 27,266)( 28,268)( 29,270)( 30,269)( 31,271)( 32,273)
( 33,272)( 34,274)( 35,276)( 36,275)( 37,277)( 38,279)( 39,278)( 40,280)
( 41,282)( 42,281)( 43,283)( 44,285)( 45,284)( 46,286)( 47,288)( 48,287)
( 49,193)( 50,195)( 51,194)( 52,196)( 53,198)( 54,197)( 55,199)( 56,201)
( 57,200)( 58,202)( 59,204)( 60,203)( 61,205)( 62,207)( 63,206)( 64,208)
( 65,210)( 66,209)( 67,211)( 68,213)( 69,212)( 70,214)( 71,216)( 72,215)
( 73,217)( 74,219)( 75,218)( 76,220)( 77,222)( 78,221)( 79,223)( 80,225)
( 81,224)( 82,226)( 83,228)( 84,227)( 85,229)( 86,231)( 87,230)( 88,232)
( 89,234)( 90,233)( 91,235)( 92,237)( 93,236)( 94,238)( 95,240)( 96,239)
( 97,343)( 98,345)( 99,344)(100,346)(101,348)(102,347)(103,337)(104,339)
(105,338)(106,340)(107,342)(108,341)(109,355)(110,357)(111,356)(112,358)
(113,360)(114,359)(115,349)(116,351)(117,350)(118,352)(119,354)(120,353)
(121,367)(122,369)(123,368)(124,370)(125,372)(126,371)(127,361)(128,363)
(129,362)(130,364)(131,366)(132,365)(133,379)(134,381)(135,380)(136,382)
(137,384)(138,383)(139,373)(140,375)(141,374)(142,376)(143,378)(144,377)
(145,295)(146,297)(147,296)(148,298)(149,300)(150,299)(151,289)(152,291)
(153,290)(154,292)(155,294)(156,293)(157,307)(158,309)(159,308)(160,310)
(161,312)(162,311)(163,301)(164,303)(165,302)(166,304)(167,306)(168,305)
(169,319)(170,321)(171,320)(172,322)(173,324)(174,323)(175,313)(176,315)
(177,314)(178,316)(179,318)(180,317)(181,331)(182,333)(183,332)(184,334)
(185,336)(186,335)(187,325)(188,327)(189,326)(190,328)(191,330)(192,329);;
s1 := ( 1,147)( 2,146)( 3,145)( 4,150)( 5,149)( 6,148)( 7,153)( 8,152)
( 9,151)( 10,156)( 11,155)( 12,154)( 13,162)( 14,161)( 15,160)( 16,159)
( 17,158)( 18,157)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)( 24,163)
( 25,174)( 26,173)( 27,172)( 28,171)( 29,170)( 30,169)( 31,180)( 32,179)
( 33,178)( 34,177)( 35,176)( 36,175)( 37,183)( 38,182)( 39,181)( 40,186)
( 41,185)( 42,184)( 43,189)( 44,188)( 45,187)( 46,192)( 47,191)( 48,190)
( 49, 99)( 50, 98)( 51, 97)( 52,102)( 53,101)( 54,100)( 55,105)( 56,104)
( 57,103)( 58,108)( 59,107)( 60,106)( 61,114)( 62,113)( 63,112)( 64,111)
( 65,110)( 66,109)( 67,120)( 68,119)( 69,118)( 70,117)( 71,116)( 72,115)
( 73,126)( 74,125)( 75,124)( 76,123)( 77,122)( 78,121)( 79,132)( 80,131)
( 81,130)( 82,129)( 83,128)( 84,127)( 85,135)( 86,134)( 87,133)( 88,138)
( 89,137)( 90,136)( 91,141)( 92,140)( 93,139)( 94,144)( 95,143)( 96,142)
(193,339)(194,338)(195,337)(196,342)(197,341)(198,340)(199,345)(200,344)
(201,343)(202,348)(203,347)(204,346)(205,354)(206,353)(207,352)(208,351)
(209,350)(210,349)(211,360)(212,359)(213,358)(214,357)(215,356)(216,355)
(217,366)(218,365)(219,364)(220,363)(221,362)(222,361)(223,372)(224,371)
(225,370)(226,369)(227,368)(228,367)(229,375)(230,374)(231,373)(232,378)
(233,377)(234,376)(235,381)(236,380)(237,379)(238,384)(239,383)(240,382)
(241,291)(242,290)(243,289)(244,294)(245,293)(246,292)(247,297)(248,296)
(249,295)(250,300)(251,299)(252,298)(253,306)(254,305)(255,304)(256,303)
(257,302)(258,301)(259,312)(260,311)(261,310)(262,309)(263,308)(264,307)
(265,318)(266,317)(267,316)(268,315)(269,314)(270,313)(271,324)(272,323)
(273,322)(274,321)(275,320)(276,319)(277,327)(278,326)(279,325)(280,330)
(281,329)(282,328)(283,333)(284,332)(285,331)(286,336)(287,335)(288,334);;
s2 := ( 13, 16)( 14, 17)( 15, 18)( 19, 22)( 20, 23)( 21, 24)( 25, 28)( 26, 29)
( 27, 30)( 31, 34)( 32, 35)( 33, 36)( 49, 73)( 50, 74)( 51, 75)( 52, 76)
( 53, 77)( 54, 78)( 55, 79)( 56, 80)( 57, 81)( 58, 82)( 59, 83)( 60, 84)
( 61, 88)( 62, 89)( 63, 90)( 64, 85)( 65, 86)( 66, 87)( 67, 94)( 68, 95)
( 69, 96)( 70, 91)( 71, 92)( 72, 93)( 97,109)( 98,110)( 99,111)(100,112)
(101,113)(102,114)(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)
(121,136)(122,137)(123,138)(124,133)(125,134)(126,135)(127,142)(128,143)
(129,144)(130,139)(131,140)(132,141)(145,181)(146,182)(147,183)(148,184)
(149,185)(150,186)(151,187)(152,188)(153,189)(154,190)(155,191)(156,192)
(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)
(165,177)(166,178)(167,179)(168,180)(193,217)(194,218)(195,219)(196,220)
(197,221)(198,222)(199,223)(200,224)(201,225)(202,226)(203,227)(204,228)
(205,232)(206,233)(207,234)(208,229)(209,230)(210,231)(211,238)(212,239)
(213,240)(214,235)(215,236)(216,237)(253,256)(254,257)(255,258)(259,262)
(260,263)(261,264)(265,268)(266,269)(267,270)(271,274)(272,275)(273,276)
(289,325)(290,326)(291,327)(292,328)(293,329)(294,330)(295,331)(296,332)
(297,333)(298,334)(299,335)(300,336)(301,313)(302,314)(303,315)(304,316)
(305,317)(306,318)(307,319)(308,320)(309,321)(310,322)(311,323)(312,324)
(337,349)(338,350)(339,351)(340,352)(341,353)(342,354)(343,355)(344,356)
(345,357)(346,358)(347,359)(348,360)(361,376)(362,377)(363,378)(364,373)
(365,374)(366,375)(367,382)(368,383)(369,384)(370,379)(371,380)(372,381);;
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, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)( 32, 83)
( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 37, 88)( 38, 89)( 39, 90)( 40, 85)
( 41, 86)( 42, 87)( 43, 94)( 44, 95)( 45, 96)( 46, 91)( 47, 92)( 48, 93)
( 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)
(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)(128,179)
(129,180)(130,175)(131,176)(132,177)(133,184)(134,185)(135,186)(136,181)
(137,182)(138,183)(139,190)(140,191)(141,192)(142,187)(143,188)(144,189)
(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)
(217,268)(218,269)(219,270)(220,265)(221,266)(222,267)(223,274)(224,275)
(225,276)(226,271)(227,272)(228,273)(229,280)(230,281)(231,282)(232,277)
(233,278)(234,279)(235,286)(236,287)(237,288)(238,283)(239,284)(240,285)
(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)
(313,364)(314,365)(315,366)(316,361)(317,362)(318,363)(319,370)(320,371)
(321,372)(322,367)(323,368)(324,369)(325,376)(326,377)(327,378)(328,373)
(329,374)(330,375)(331,382)(332,383)(333,384)(334,379)(335,380)(336,381);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
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)!( 1,241)( 2,243)( 3,242)( 4,244)( 5,246)( 6,245)( 7,247)
( 8,249)( 9,248)( 10,250)( 11,252)( 12,251)( 13,253)( 14,255)( 15,254)
( 16,256)( 17,258)( 18,257)( 19,259)( 20,261)( 21,260)( 22,262)( 23,264)
( 24,263)( 25,265)( 26,267)( 27,266)( 28,268)( 29,270)( 30,269)( 31,271)
( 32,273)( 33,272)( 34,274)( 35,276)( 36,275)( 37,277)( 38,279)( 39,278)
( 40,280)( 41,282)( 42,281)( 43,283)( 44,285)( 45,284)( 46,286)( 47,288)
( 48,287)( 49,193)( 50,195)( 51,194)( 52,196)( 53,198)( 54,197)( 55,199)
( 56,201)( 57,200)( 58,202)( 59,204)( 60,203)( 61,205)( 62,207)( 63,206)
( 64,208)( 65,210)( 66,209)( 67,211)( 68,213)( 69,212)( 70,214)( 71,216)
( 72,215)( 73,217)( 74,219)( 75,218)( 76,220)( 77,222)( 78,221)( 79,223)
( 80,225)( 81,224)( 82,226)( 83,228)( 84,227)( 85,229)( 86,231)( 87,230)
( 88,232)( 89,234)( 90,233)( 91,235)( 92,237)( 93,236)( 94,238)( 95,240)
( 96,239)( 97,343)( 98,345)( 99,344)(100,346)(101,348)(102,347)(103,337)
(104,339)(105,338)(106,340)(107,342)(108,341)(109,355)(110,357)(111,356)
(112,358)(113,360)(114,359)(115,349)(116,351)(117,350)(118,352)(119,354)
(120,353)(121,367)(122,369)(123,368)(124,370)(125,372)(126,371)(127,361)
(128,363)(129,362)(130,364)(131,366)(132,365)(133,379)(134,381)(135,380)
(136,382)(137,384)(138,383)(139,373)(140,375)(141,374)(142,376)(143,378)
(144,377)(145,295)(146,297)(147,296)(148,298)(149,300)(150,299)(151,289)
(152,291)(153,290)(154,292)(155,294)(156,293)(157,307)(158,309)(159,308)
(160,310)(161,312)(162,311)(163,301)(164,303)(165,302)(166,304)(167,306)
(168,305)(169,319)(170,321)(171,320)(172,322)(173,324)(174,323)(175,313)
(176,315)(177,314)(178,316)(179,318)(180,317)(181,331)(182,333)(183,332)
(184,334)(185,336)(186,335)(187,325)(188,327)(189,326)(190,328)(191,330)
(192,329);
s1 := Sym(384)!( 1,147)( 2,146)( 3,145)( 4,150)( 5,149)( 6,148)( 7,153)
( 8,152)( 9,151)( 10,156)( 11,155)( 12,154)( 13,162)( 14,161)( 15,160)
( 16,159)( 17,158)( 18,157)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)
( 24,163)( 25,174)( 26,173)( 27,172)( 28,171)( 29,170)( 30,169)( 31,180)
( 32,179)( 33,178)( 34,177)( 35,176)( 36,175)( 37,183)( 38,182)( 39,181)
( 40,186)( 41,185)( 42,184)( 43,189)( 44,188)( 45,187)( 46,192)( 47,191)
( 48,190)( 49, 99)( 50, 98)( 51, 97)( 52,102)( 53,101)( 54,100)( 55,105)
( 56,104)( 57,103)( 58,108)( 59,107)( 60,106)( 61,114)( 62,113)( 63,112)
( 64,111)( 65,110)( 66,109)( 67,120)( 68,119)( 69,118)( 70,117)( 71,116)
( 72,115)( 73,126)( 74,125)( 75,124)( 76,123)( 77,122)( 78,121)( 79,132)
( 80,131)( 81,130)( 82,129)( 83,128)( 84,127)( 85,135)( 86,134)( 87,133)
( 88,138)( 89,137)( 90,136)( 91,141)( 92,140)( 93,139)( 94,144)( 95,143)
( 96,142)(193,339)(194,338)(195,337)(196,342)(197,341)(198,340)(199,345)
(200,344)(201,343)(202,348)(203,347)(204,346)(205,354)(206,353)(207,352)
(208,351)(209,350)(210,349)(211,360)(212,359)(213,358)(214,357)(215,356)
(216,355)(217,366)(218,365)(219,364)(220,363)(221,362)(222,361)(223,372)
(224,371)(225,370)(226,369)(227,368)(228,367)(229,375)(230,374)(231,373)
(232,378)(233,377)(234,376)(235,381)(236,380)(237,379)(238,384)(239,383)
(240,382)(241,291)(242,290)(243,289)(244,294)(245,293)(246,292)(247,297)
(248,296)(249,295)(250,300)(251,299)(252,298)(253,306)(254,305)(255,304)
(256,303)(257,302)(258,301)(259,312)(260,311)(261,310)(262,309)(263,308)
(264,307)(265,318)(266,317)(267,316)(268,315)(269,314)(270,313)(271,324)
(272,323)(273,322)(274,321)(275,320)(276,319)(277,327)(278,326)(279,325)
(280,330)(281,329)(282,328)(283,333)(284,332)(285,331)(286,336)(287,335)
(288,334);
s2 := Sym(384)!( 13, 16)( 14, 17)( 15, 18)( 19, 22)( 20, 23)( 21, 24)( 25, 28)
( 26, 29)( 27, 30)( 31, 34)( 32, 35)( 33, 36)( 49, 73)( 50, 74)( 51, 75)
( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)( 57, 81)( 58, 82)( 59, 83)
( 60, 84)( 61, 88)( 62, 89)( 63, 90)( 64, 85)( 65, 86)( 66, 87)( 67, 94)
( 68, 95)( 69, 96)( 70, 91)( 71, 92)( 72, 93)( 97,109)( 98,110)( 99,111)
(100,112)(101,113)(102,114)(103,115)(104,116)(105,117)(106,118)(107,119)
(108,120)(121,136)(122,137)(123,138)(124,133)(125,134)(126,135)(127,142)
(128,143)(129,144)(130,139)(131,140)(132,141)(145,181)(146,182)(147,183)
(148,184)(149,185)(150,186)(151,187)(152,188)(153,189)(154,190)(155,191)
(156,192)(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)
(164,176)(165,177)(166,178)(167,179)(168,180)(193,217)(194,218)(195,219)
(196,220)(197,221)(198,222)(199,223)(200,224)(201,225)(202,226)(203,227)
(204,228)(205,232)(206,233)(207,234)(208,229)(209,230)(210,231)(211,238)
(212,239)(213,240)(214,235)(215,236)(216,237)(253,256)(254,257)(255,258)
(259,262)(260,263)(261,264)(265,268)(266,269)(267,270)(271,274)(272,275)
(273,276)(289,325)(290,326)(291,327)(292,328)(293,329)(294,330)(295,331)
(296,332)(297,333)(298,334)(299,335)(300,336)(301,313)(302,314)(303,315)
(304,316)(305,317)(306,318)(307,319)(308,320)(309,321)(310,322)(311,323)
(312,324)(337,349)(338,350)(339,351)(340,352)(341,353)(342,354)(343,355)
(344,356)(345,357)(346,358)(347,359)(348,360)(361,376)(362,377)(363,378)
(364,373)(365,374)(366,375)(367,382)(368,383)(369,384)(370,379)(371,380)
(372,381);
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, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)
( 32, 83)( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 37, 88)( 38, 89)( 39, 90)
( 40, 85)( 41, 86)( 42, 87)( 43, 94)( 44, 95)( 45, 96)( 46, 91)( 47, 92)
( 48, 93)( 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)(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)
(128,179)(129,180)(130,175)(131,176)(132,177)(133,184)(134,185)(135,186)
(136,181)(137,182)(138,183)(139,190)(140,191)(141,192)(142,187)(143,188)
(144,189)(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)(217,268)(218,269)(219,270)(220,265)(221,266)(222,267)(223,274)
(224,275)(225,276)(226,271)(227,272)(228,273)(229,280)(230,281)(231,282)
(232,277)(233,278)(234,279)(235,286)(236,287)(237,288)(238,283)(239,284)
(240,285)(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)(313,364)(314,365)(315,366)(316,361)(317,362)(318,363)(319,370)
(320,371)(321,372)(322,367)(323,368)(324,369)(325,376)(326,377)(327,378)
(328,373)(329,374)(330,375)(331,382)(332,383)(333,384)(334,379)(335,380)
(336,381);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 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