Polytope of Type {4,12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,8}*768b
if this polytope has a name.
Group : SmallGroup(768,200907)
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}*384b
3-fold quotients : {4,4,8}*256b
4-fold quotients : {2,12,4}*192a, {4,12,2}*192a, {4,6,4}*192a
6-fold quotients : {4,4,4}*128, {2,4,8}*128b
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
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 := ( 1,145)( 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);;
s2 := ( 1, 3)( 4, 6)( 7, 9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)( 19, 24)
( 20, 23)( 21, 22)( 25, 30)( 26, 29)( 27, 28)( 31, 36)( 32, 35)( 33, 34)
( 37, 39)( 40, 42)( 43, 45)( 46, 48)( 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, 90)( 62, 89)( 63, 88)( 64, 87)( 65, 86)( 66, 85)( 67, 96)( 68, 95)
( 69, 94)( 70, 93)( 71, 92)( 72, 91)( 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)
(205,234)(206,233)(207,232)(208,231)(209,230)(210,229)(211,240)(212,239)
(213,238)(214,237)(215,236)(216,235)(241,243)(244,246)(247,249)(250,252)
(253,258)(254,257)(255,256)(259,264)(260,263)(261,262)(265,270)(266,269)
(267,268)(271,276)(272,275)(273,274)(277,279)(280,282)(283,285)(286,288)
(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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
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)!( 1,145)( 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);
s2 := Sym(384)!( 1, 3)( 4, 6)( 7, 9)( 10, 12)( 13, 18)( 14, 17)( 15, 16)
( 19, 24)( 20, 23)( 21, 22)( 25, 30)( 26, 29)( 27, 28)( 31, 36)( 32, 35)
( 33, 34)( 37, 39)( 40, 42)( 43, 45)( 46, 48)( 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, 90)( 62, 89)( 63, 88)( 64, 87)( 65, 86)( 66, 85)( 67, 96)
( 68, 95)( 69, 94)( 70, 93)( 71, 92)( 72, 91)( 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)(205,234)(206,233)(207,232)(208,231)(209,230)(210,229)(211,240)
(212,239)(213,238)(214,237)(215,236)(216,235)(241,243)(244,246)(247,249)
(250,252)(253,258)(254,257)(255,256)(259,264)(260,263)(261,262)(265,270)
(266,269)(267,268)(271,276)(272,275)(273,274)(277,279)(280,282)(283,285)
(286,288)(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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
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