Polytope of Type {4,12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,8}*768a
Also Known As : {{4,12|2},{12,8|2}}. if this polytope has another name.
Group : SmallGroup(768,200567)
Rank : 4
Schlafli Type : {4,12,8}
Number of vertices, edges, etc : 4, 24, 48, 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 : {4,12,4}*384a, {2,12,8}*384a, {4,6,8}*384a
3-fold quotients : {4,4,8}*256a
4-fold quotients : {2,12,4}*192a, {4,12,2}*192a, {4,6,4}*192a, {2,6,8}*192
6-fold quotients : {4,4,4}*128, {2,4,8}*128a, {4,2,8}*128
8-fold quotients : {2,12,2}*96, {2,6,4}*96a, {4,6,2}*96a
12-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,2,8}*64
16-fold quotients : {2,6,2}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
32-fold quotients : {2,3,2}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)( 8,248)
( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)( 80,224)
( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)( 88,232)
( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)( 96,240)
( 97,343)( 98,344)( 99,345)(100,346)(101,347)(102,348)(103,337)(104,338)
(105,339)(106,340)(107,341)(108,342)(109,355)(110,356)(111,357)(112,358)
(113,359)(114,360)(115,349)(116,350)(117,351)(118,352)(119,353)(120,354)
(121,367)(122,368)(123,369)(124,370)(125,371)(126,372)(127,361)(128,362)
(129,363)(130,364)(131,365)(132,366)(133,379)(134,380)(135,381)(136,382)
(137,383)(138,384)(139,373)(140,374)(141,375)(142,376)(143,377)(144,378)
(145,295)(146,296)(147,297)(148,298)(149,299)(150,300)(151,289)(152,290)
(153,291)(154,292)(155,293)(156,294)(157,307)(158,308)(159,309)(160,310)
(161,311)(162,312)(163,301)(164,302)(165,303)(166,304)(167,305)(168,306)
(169,319)(170,320)(171,321)(172,322)(173,323)(174,324)(175,313)(176,314)
(177,315)(178,316)(179,317)(180,318)(181,331)(182,332)(183,333)(184,334)
(185,335)(186,336)(187,325)(188,326)(189,327)(190,328)(191,329)(192,330);;
s1 := ( 1, 97)( 2, 99)( 3, 98)( 4,100)( 5,102)( 6,101)( 7,103)( 8,105)
( 9,104)( 10,106)( 11,108)( 12,107)( 13,109)( 14,111)( 15,110)( 16,112)
( 17,114)( 18,113)( 19,115)( 20,117)( 21,116)( 22,118)( 23,120)( 24,119)
( 25,121)( 26,123)( 27,122)( 28,124)( 29,126)( 30,125)( 31,127)( 32,129)
( 33,128)( 34,130)( 35,132)( 36,131)( 37,133)( 38,135)( 39,134)( 40,136)
( 41,138)( 42,137)( 43,139)( 44,141)( 45,140)( 46,142)( 47,144)( 48,143)
( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)( 56,153)
( 57,152)( 58,154)( 59,156)( 60,155)( 61,157)( 62,159)( 63,158)( 64,160)
( 65,162)( 66,161)( 67,163)( 68,165)( 69,164)( 70,166)( 71,168)( 72,167)
( 73,169)( 74,171)( 75,170)( 76,172)( 77,174)( 78,173)( 79,175)( 80,177)
( 81,176)( 82,178)( 83,180)( 84,179)( 85,181)( 86,183)( 87,182)( 88,184)
( 89,186)( 90,185)( 91,187)( 92,189)( 93,188)( 94,190)( 95,192)( 96,191)
(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,295)(200,297)
(201,296)(202,298)(203,300)(204,299)(205,301)(206,303)(207,302)(208,304)
(209,306)(210,305)(211,307)(212,309)(213,308)(214,310)(215,312)(216,311)
(217,313)(218,315)(219,314)(220,316)(221,318)(222,317)(223,319)(224,321)
(225,320)(226,322)(227,324)(228,323)(229,325)(230,327)(231,326)(232,328)
(233,330)(234,329)(235,331)(236,333)(237,332)(238,334)(239,336)(240,335)
(241,337)(242,339)(243,338)(244,340)(245,342)(246,341)(247,343)(248,345)
(249,344)(250,346)(251,348)(252,347)(253,349)(254,351)(255,350)(256,352)
(257,354)(258,353)(259,355)(260,357)(261,356)(262,358)(263,360)(264,359)
(265,361)(266,363)(267,362)(268,364)(269,366)(270,365)(271,367)(272,369)
(273,368)(274,370)(275,372)(276,371)(277,373)(278,375)(279,374)(280,376)
(281,378)(282,377)(283,379)(284,381)(285,380)(286,382)(287,384)(288,383);;
s2 := ( 1, 3)( 4, 6)( 7, 9)( 10, 12)( 13, 15)( 16, 18)( 19, 21)( 22, 24)
( 25, 30)( 26, 29)( 27, 28)( 31, 36)( 32, 35)( 33, 34)( 37, 42)( 38, 41)
( 39, 40)( 43, 48)( 44, 47)( 45, 46)( 49, 75)( 50, 74)( 51, 73)( 52, 78)
( 53, 77)( 54, 76)( 55, 81)( 56, 80)( 57, 79)( 58, 84)( 59, 83)( 60, 82)
( 61, 87)( 62, 86)( 63, 85)( 64, 90)( 65, 89)( 66, 88)( 67, 93)( 68, 92)
( 69, 91)( 70, 96)( 71, 95)( 72, 94)( 97,111)( 98,110)( 99,109)(100,114)
(101,113)(102,112)(103,117)(104,116)(105,115)(106,120)(107,119)(108,118)
(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)(127,144)(128,143)
(129,142)(130,141)(131,140)(132,139)(145,183)(146,182)(147,181)(148,186)
(149,185)(150,184)(151,189)(152,188)(153,187)(154,192)(155,191)(156,190)
(157,171)(158,170)(159,169)(160,174)(161,173)(162,172)(163,177)(164,176)
(165,175)(166,180)(167,179)(168,178)(193,219)(194,218)(195,217)(196,222)
(197,221)(198,220)(199,225)(200,224)(201,223)(202,228)(203,227)(204,226)
(205,231)(206,230)(207,229)(208,234)(209,233)(210,232)(211,237)(212,236)
(213,235)(214,240)(215,239)(216,238)(241,243)(244,246)(247,249)(250,252)
(253,255)(256,258)(259,261)(262,264)(265,270)(266,269)(267,268)(271,276)
(272,275)(273,274)(277,282)(278,281)(279,280)(283,288)(284,287)(285,286)
(289,327)(290,326)(291,325)(292,330)(293,329)(294,328)(295,333)(296,332)
(297,331)(298,336)(299,335)(300,334)(301,315)(302,314)(303,313)(304,318)
(305,317)(306,316)(307,321)(308,320)(309,319)(310,324)(311,323)(312,322)
(337,351)(338,350)(339,349)(340,354)(341,353)(342,352)(343,357)(344,356)
(345,355)(346,360)(347,359)(348,358)(361,378)(362,377)(363,376)(364,375)
(365,374)(366,373)(367,384)(368,383)(369,382)(370,381)(371,380)(372,379);;
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)
( 8,248)( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)
( 80,224)( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)
( 88,232)( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)
( 96,240)( 97,343)( 98,344)( 99,345)(100,346)(101,347)(102,348)(103,337)
(104,338)(105,339)(106,340)(107,341)(108,342)(109,355)(110,356)(111,357)
(112,358)(113,359)(114,360)(115,349)(116,350)(117,351)(118,352)(119,353)
(120,354)(121,367)(122,368)(123,369)(124,370)(125,371)(126,372)(127,361)
(128,362)(129,363)(130,364)(131,365)(132,366)(133,379)(134,380)(135,381)
(136,382)(137,383)(138,384)(139,373)(140,374)(141,375)(142,376)(143,377)
(144,378)(145,295)(146,296)(147,297)(148,298)(149,299)(150,300)(151,289)
(152,290)(153,291)(154,292)(155,293)(156,294)(157,307)(158,308)(159,309)
(160,310)(161,311)(162,312)(163,301)(164,302)(165,303)(166,304)(167,305)
(168,306)(169,319)(170,320)(171,321)(172,322)(173,323)(174,324)(175,313)
(176,314)(177,315)(178,316)(179,317)(180,318)(181,331)(182,332)(183,333)
(184,334)(185,335)(186,336)(187,325)(188,326)(189,327)(190,328)(191,329)
(192,330);
s1 := Sym(384)!( 1, 97)( 2, 99)( 3, 98)( 4,100)( 5,102)( 6,101)( 7,103)
( 8,105)( 9,104)( 10,106)( 11,108)( 12,107)( 13,109)( 14,111)( 15,110)
( 16,112)( 17,114)( 18,113)( 19,115)( 20,117)( 21,116)( 22,118)( 23,120)
( 24,119)( 25,121)( 26,123)( 27,122)( 28,124)( 29,126)( 30,125)( 31,127)
( 32,129)( 33,128)( 34,130)( 35,132)( 36,131)( 37,133)( 38,135)( 39,134)
( 40,136)( 41,138)( 42,137)( 43,139)( 44,141)( 45,140)( 46,142)( 47,144)
( 48,143)( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)
( 56,153)( 57,152)( 58,154)( 59,156)( 60,155)( 61,157)( 62,159)( 63,158)
( 64,160)( 65,162)( 66,161)( 67,163)( 68,165)( 69,164)( 70,166)( 71,168)
( 72,167)( 73,169)( 74,171)( 75,170)( 76,172)( 77,174)( 78,173)( 79,175)
( 80,177)( 81,176)( 82,178)( 83,180)( 84,179)( 85,181)( 86,183)( 87,182)
( 88,184)( 89,186)( 90,185)( 91,187)( 92,189)( 93,188)( 94,190)( 95,192)
( 96,191)(193,289)(194,291)(195,290)(196,292)(197,294)(198,293)(199,295)
(200,297)(201,296)(202,298)(203,300)(204,299)(205,301)(206,303)(207,302)
(208,304)(209,306)(210,305)(211,307)(212,309)(213,308)(214,310)(215,312)
(216,311)(217,313)(218,315)(219,314)(220,316)(221,318)(222,317)(223,319)
(224,321)(225,320)(226,322)(227,324)(228,323)(229,325)(230,327)(231,326)
(232,328)(233,330)(234,329)(235,331)(236,333)(237,332)(238,334)(239,336)
(240,335)(241,337)(242,339)(243,338)(244,340)(245,342)(246,341)(247,343)
(248,345)(249,344)(250,346)(251,348)(252,347)(253,349)(254,351)(255,350)
(256,352)(257,354)(258,353)(259,355)(260,357)(261,356)(262,358)(263,360)
(264,359)(265,361)(266,363)(267,362)(268,364)(269,366)(270,365)(271,367)
(272,369)(273,368)(274,370)(275,372)(276,371)(277,373)(278,375)(279,374)
(280,376)(281,378)(282,377)(283,379)(284,381)(285,380)(286,382)(287,384)
(288,383);
s2 := Sym(384)!( 1, 3)( 4, 6)( 7, 9)( 10, 12)( 13, 15)( 16, 18)( 19, 21)
( 22, 24)( 25, 30)( 26, 29)( 27, 28)( 31, 36)( 32, 35)( 33, 34)( 37, 42)
( 38, 41)( 39, 40)( 43, 48)( 44, 47)( 45, 46)( 49, 75)( 50, 74)( 51, 73)
( 52, 78)( 53, 77)( 54, 76)( 55, 81)( 56, 80)( 57, 79)( 58, 84)( 59, 83)
( 60, 82)( 61, 87)( 62, 86)( 63, 85)( 64, 90)( 65, 89)( 66, 88)( 67, 93)
( 68, 92)( 69, 91)( 70, 96)( 71, 95)( 72, 94)( 97,111)( 98,110)( 99,109)
(100,114)(101,113)(102,112)(103,117)(104,116)(105,115)(106,120)(107,119)
(108,118)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)(127,144)
(128,143)(129,142)(130,141)(131,140)(132,139)(145,183)(146,182)(147,181)
(148,186)(149,185)(150,184)(151,189)(152,188)(153,187)(154,192)(155,191)
(156,190)(157,171)(158,170)(159,169)(160,174)(161,173)(162,172)(163,177)
(164,176)(165,175)(166,180)(167,179)(168,178)(193,219)(194,218)(195,217)
(196,222)(197,221)(198,220)(199,225)(200,224)(201,223)(202,228)(203,227)
(204,226)(205,231)(206,230)(207,229)(208,234)(209,233)(210,232)(211,237)
(212,236)(213,235)(214,240)(215,239)(216,238)(241,243)(244,246)(247,249)
(250,252)(253,255)(256,258)(259,261)(262,264)(265,270)(266,269)(267,268)
(271,276)(272,275)(273,274)(277,282)(278,281)(279,280)(283,288)(284,287)
(285,286)(289,327)(290,326)(291,325)(292,330)(293,329)(294,328)(295,333)
(296,332)(297,331)(298,336)(299,335)(300,334)(301,315)(302,314)(303,313)
(304,318)(305,317)(306,316)(307,321)(308,320)(309,319)(310,324)(311,323)
(312,322)(337,351)(338,350)(339,349)(340,354)(341,353)(342,352)(343,357)
(344,356)(345,355)(346,360)(347,359)(348,358)(361,378)(362,377)(363,376)
(364,375)(365,374)(366,373)(367,384)(368,383)(369,382)(370,381)(371,380)
(372,379);
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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope