Polytope of Type {8,4,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,12}*768b
if this polytope has a name.
Group : SmallGroup(768,200904)
Rank : 4
Schlafli Type : {8,4,12}
Number of vertices, edges, etc : 8, 16, 24, 12
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 : {4,4,12}*384, {8,4,6}*384b
3-fold quotients : {8,4,4}*256b
4-fold quotients : {2,4,12}*192a, {4,2,12}*192, {4,4,6}*192
6-fold quotients : {4,4,4}*128, {8,4,2}*128b
8-fold quotients : {2,2,12}*96, {2,4,6}*96a, {4,2,6}*96
12-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
16-fold quotients : {4,2,3}*48, {2,2,6}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
32-fold quotients : {2,2,3}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 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);;
s2 := ( 1,145)( 2,147)( 3,146)( 4,148)( 5,150)( 6,149)( 7,151)( 8,153)
( 9,152)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)( 16,157)
( 17,159)( 18,158)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)( 24,164)
( 25,172)( 26,174)( 27,173)( 28,169)( 29,171)( 30,170)( 31,178)( 32,180)
( 33,179)( 34,175)( 35,177)( 36,176)( 37,181)( 38,183)( 39,182)( 40,184)
( 41,186)( 42,185)( 43,187)( 44,189)( 45,188)( 46,190)( 47,192)( 48,191)
( 49, 97)( 50, 99)( 51, 98)( 52,100)( 53,102)( 54,101)( 55,103)( 56,105)
( 57,104)( 58,106)( 59,108)( 60,107)( 61,112)( 62,114)( 63,113)( 64,109)
( 65,111)( 66,110)( 67,118)( 68,120)( 69,119)( 70,115)( 71,117)( 72,116)
( 73,124)( 74,126)( 75,125)( 76,121)( 77,123)( 78,122)( 79,130)( 80,132)
( 81,131)( 82,127)( 83,129)( 84,128)( 85,133)( 86,135)( 87,134)( 88,136)
( 89,138)( 90,137)( 91,139)( 92,141)( 93,140)( 94,142)( 95,144)( 96,143)
(193,337)(194,339)(195,338)(196,340)(197,342)(198,341)(199,343)(200,345)
(201,344)(202,346)(203,348)(204,347)(205,352)(206,354)(207,353)(208,349)
(209,351)(210,350)(211,358)(212,360)(213,359)(214,355)(215,357)(216,356)
(217,364)(218,366)(219,365)(220,361)(221,363)(222,362)(223,370)(224,372)
(225,371)(226,367)(227,369)(228,368)(229,373)(230,375)(231,374)(232,376)
(233,378)(234,377)(235,379)(236,381)(237,380)(238,382)(239,384)(240,383)
(241,289)(242,291)(243,290)(244,292)(245,294)(246,293)(247,295)(248,297)
(249,296)(250,298)(251,300)(252,299)(253,304)(254,306)(255,305)(256,301)
(257,303)(258,302)(259,310)(260,312)(261,311)(262,307)(263,309)(264,308)
(265,316)(266,318)(267,317)(268,313)(269,315)(270,314)(271,322)(272,324)
(273,323)(274,319)(275,321)(276,320)(277,325)(278,327)(279,326)(280,328)
(281,330)(282,329)(283,331)(284,333)(285,332)(286,334)(287,336)(288,335);;
s3 := ( 1,243)( 2,242)( 3,241)( 4,246)( 5,245)( 6,244)( 7,249)( 8,248)
( 9,247)( 10,252)( 11,251)( 12,250)( 13,255)( 14,254)( 15,253)( 16,258)
( 17,257)( 18,256)( 19,261)( 20,260)( 21,259)( 22,264)( 23,263)( 24,262)
( 25,267)( 26,266)( 27,265)( 28,270)( 29,269)( 30,268)( 31,273)( 32,272)
( 33,271)( 34,276)( 35,275)( 36,274)( 37,279)( 38,278)( 39,277)( 40,282)
( 41,281)( 42,280)( 43,285)( 44,284)( 45,283)( 46,288)( 47,287)( 48,286)
( 49,195)( 50,194)( 51,193)( 52,198)( 53,197)( 54,196)( 55,201)( 56,200)
( 57,199)( 58,204)( 59,203)( 60,202)( 61,207)( 62,206)( 63,205)( 64,210)
( 65,209)( 66,208)( 67,213)( 68,212)( 69,211)( 70,216)( 71,215)( 72,214)
( 73,219)( 74,218)( 75,217)( 76,222)( 77,221)( 78,220)( 79,225)( 80,224)
( 81,223)( 82,228)( 83,227)( 84,226)( 85,231)( 86,230)( 87,229)( 88,234)
( 89,233)( 90,232)( 91,237)( 92,236)( 93,235)( 94,240)( 95,239)( 96,238)
( 97,345)( 98,344)( 99,343)(100,348)(101,347)(102,346)(103,339)(104,338)
(105,337)(106,342)(107,341)(108,340)(109,357)(110,356)(111,355)(112,360)
(113,359)(114,358)(115,351)(116,350)(117,349)(118,354)(119,353)(120,352)
(121,369)(122,368)(123,367)(124,372)(125,371)(126,370)(127,363)(128,362)
(129,361)(130,366)(131,365)(132,364)(133,381)(134,380)(135,379)(136,384)
(137,383)(138,382)(139,375)(140,374)(141,373)(142,378)(143,377)(144,376)
(145,297)(146,296)(147,295)(148,300)(149,299)(150,298)(151,291)(152,290)
(153,289)(154,294)(155,293)(156,292)(157,309)(158,308)(159,307)(160,312)
(161,311)(162,310)(163,303)(164,302)(165,301)(166,306)(167,305)(168,304)
(169,321)(170,320)(171,319)(172,324)(173,323)(174,322)(175,315)(176,314)
(177,313)(178,318)(179,317)(180,316)(181,333)(182,332)(183,331)(184,336)
(185,335)(186,334)(187,327)(188,326)(189,325)(190,330)(191,329)(192,328);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := 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);
s2 := Sym(384)!( 1,145)( 2,147)( 3,146)( 4,148)( 5,150)( 6,149)( 7,151)
( 8,153)( 9,152)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)
( 16,157)( 17,159)( 18,158)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)
( 24,164)( 25,172)( 26,174)( 27,173)( 28,169)( 29,171)( 30,170)( 31,178)
( 32,180)( 33,179)( 34,175)( 35,177)( 36,176)( 37,181)( 38,183)( 39,182)
( 40,184)( 41,186)( 42,185)( 43,187)( 44,189)( 45,188)( 46,190)( 47,192)
( 48,191)( 49, 97)( 50, 99)( 51, 98)( 52,100)( 53,102)( 54,101)( 55,103)
( 56,105)( 57,104)( 58,106)( 59,108)( 60,107)( 61,112)( 62,114)( 63,113)
( 64,109)( 65,111)( 66,110)( 67,118)( 68,120)( 69,119)( 70,115)( 71,117)
( 72,116)( 73,124)( 74,126)( 75,125)( 76,121)( 77,123)( 78,122)( 79,130)
( 80,132)( 81,131)( 82,127)( 83,129)( 84,128)( 85,133)( 86,135)( 87,134)
( 88,136)( 89,138)( 90,137)( 91,139)( 92,141)( 93,140)( 94,142)( 95,144)
( 96,143)(193,337)(194,339)(195,338)(196,340)(197,342)(198,341)(199,343)
(200,345)(201,344)(202,346)(203,348)(204,347)(205,352)(206,354)(207,353)
(208,349)(209,351)(210,350)(211,358)(212,360)(213,359)(214,355)(215,357)
(216,356)(217,364)(218,366)(219,365)(220,361)(221,363)(222,362)(223,370)
(224,372)(225,371)(226,367)(227,369)(228,368)(229,373)(230,375)(231,374)
(232,376)(233,378)(234,377)(235,379)(236,381)(237,380)(238,382)(239,384)
(240,383)(241,289)(242,291)(243,290)(244,292)(245,294)(246,293)(247,295)
(248,297)(249,296)(250,298)(251,300)(252,299)(253,304)(254,306)(255,305)
(256,301)(257,303)(258,302)(259,310)(260,312)(261,311)(262,307)(263,309)
(264,308)(265,316)(266,318)(267,317)(268,313)(269,315)(270,314)(271,322)
(272,324)(273,323)(274,319)(275,321)(276,320)(277,325)(278,327)(279,326)
(280,328)(281,330)(282,329)(283,331)(284,333)(285,332)(286,334)(287,336)
(288,335);
s3 := Sym(384)!( 1,243)( 2,242)( 3,241)( 4,246)( 5,245)( 6,244)( 7,249)
( 8,248)( 9,247)( 10,252)( 11,251)( 12,250)( 13,255)( 14,254)( 15,253)
( 16,258)( 17,257)( 18,256)( 19,261)( 20,260)( 21,259)( 22,264)( 23,263)
( 24,262)( 25,267)( 26,266)( 27,265)( 28,270)( 29,269)( 30,268)( 31,273)
( 32,272)( 33,271)( 34,276)( 35,275)( 36,274)( 37,279)( 38,278)( 39,277)
( 40,282)( 41,281)( 42,280)( 43,285)( 44,284)( 45,283)( 46,288)( 47,287)
( 48,286)( 49,195)( 50,194)( 51,193)( 52,198)( 53,197)( 54,196)( 55,201)
( 56,200)( 57,199)( 58,204)( 59,203)( 60,202)( 61,207)( 62,206)( 63,205)
( 64,210)( 65,209)( 66,208)( 67,213)( 68,212)( 69,211)( 70,216)( 71,215)
( 72,214)( 73,219)( 74,218)( 75,217)( 76,222)( 77,221)( 78,220)( 79,225)
( 80,224)( 81,223)( 82,228)( 83,227)( 84,226)( 85,231)( 86,230)( 87,229)
( 88,234)( 89,233)( 90,232)( 91,237)( 92,236)( 93,235)( 94,240)( 95,239)
( 96,238)( 97,345)( 98,344)( 99,343)(100,348)(101,347)(102,346)(103,339)
(104,338)(105,337)(106,342)(107,341)(108,340)(109,357)(110,356)(111,355)
(112,360)(113,359)(114,358)(115,351)(116,350)(117,349)(118,354)(119,353)
(120,352)(121,369)(122,368)(123,367)(124,372)(125,371)(126,370)(127,363)
(128,362)(129,361)(130,366)(131,365)(132,364)(133,381)(134,380)(135,379)
(136,384)(137,383)(138,382)(139,375)(140,374)(141,373)(142,378)(143,377)
(144,376)(145,297)(146,296)(147,295)(148,300)(149,299)(150,298)(151,291)
(152,290)(153,289)(154,294)(155,293)(156,292)(157,309)(158,308)(159,307)
(160,312)(161,311)(162,310)(163,303)(164,302)(165,301)(166,306)(167,305)
(168,304)(169,321)(170,320)(171,319)(172,324)(173,323)(174,322)(175,315)
(176,314)(177,313)(178,318)(179,317)(180,316)(181,333)(182,332)(183,331)
(184,336)(185,335)(186,334)(187,327)(188,326)(189,325)(190,330)(191,329)
(192,328);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope