Polytope of Type {24,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4,4}*768b
if this polytope has a name.
Group : SmallGroup(768,200909)
Rank : 4
Schlafli Type : {24,4,4}
Number of vertices, edges, etc : 24, 48, 8, 4
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, {24,4,2}*384b
3-fold quotients : {8,4,4}*256b
4-fold quotients : {12,4,2}*192a, {12,2,4}*192, {6,4,4}*192
6-fold quotients : {4,4,4}*128, {8,4,2}*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, 49)( 2, 51)( 3, 50)( 4, 52)( 5, 54)( 6, 53)( 7, 55)( 8, 57)
( 9, 56)( 10, 58)( 11, 60)( 12, 59)( 13, 61)( 14, 63)( 15, 62)( 16, 64)
( 17, 66)( 18, 65)( 19, 67)( 20, 69)( 21, 68)( 22, 70)( 23, 72)( 24, 71)
( 25, 76)( 26, 78)( 27, 77)( 28, 73)( 29, 75)( 30, 74)( 31, 82)( 32, 84)
( 33, 83)( 34, 79)( 35, 81)( 36, 80)( 37, 88)( 38, 90)( 39, 89)( 40, 85)
( 41, 87)( 42, 86)( 43, 94)( 44, 96)( 45, 95)( 46, 91)( 47, 93)( 48, 92)
( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,151)(104,153)
(105,152)(106,154)(107,156)(108,155)(109,157)(110,159)(111,158)(112,160)
(113,162)(114,161)(115,163)(116,165)(117,164)(118,166)(119,168)(120,167)
(121,172)(122,174)(123,173)(124,169)(125,171)(126,170)(127,178)(128,180)
(129,179)(130,175)(131,177)(132,176)(133,184)(134,186)(135,185)(136,181)
(137,183)(138,182)(139,190)(140,192)(141,191)(142,187)(143,189)(144,188)
(193,241)(194,243)(195,242)(196,244)(197,246)(198,245)(199,247)(200,249)
(201,248)(202,250)(203,252)(204,251)(205,253)(206,255)(207,254)(208,256)
(209,258)(210,257)(211,259)(212,261)(213,260)(214,262)(215,264)(216,263)
(217,268)(218,270)(219,269)(220,265)(221,267)(222,266)(223,274)(224,276)
(225,275)(226,271)(227,273)(228,272)(229,280)(230,282)(231,281)(232,277)
(233,279)(234,278)(235,286)(236,288)(237,287)(238,283)(239,285)(240,284)
(289,337)(290,339)(291,338)(292,340)(293,342)(294,341)(295,343)(296,345)
(297,344)(298,346)(299,348)(300,347)(301,349)(302,351)(303,350)(304,352)
(305,354)(306,353)(307,355)(308,357)(309,356)(310,358)(311,360)(312,359)
(313,364)(314,366)(315,365)(316,361)(317,363)(318,362)(319,370)(320,372)
(321,371)(322,367)(323,369)(324,368)(325,376)(326,378)(327,377)(328,373)
(329,375)(330,374)(331,382)(332,384)(333,383)(334,379)(335,381)(336,380);;
s1 := ( 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);;
s2 := ( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)( 8,152)
( 9,153)( 10,154)( 11,155)( 12,156)( 13,160)( 14,161)( 15,162)( 16,157)
( 17,158)( 18,159)( 19,166)( 20,167)( 21,168)( 22,163)( 23,164)( 24,165)
( 25,172)( 26,173)( 27,174)( 28,169)( 29,170)( 30,171)( 31,178)( 32,179)
( 33,180)( 34,175)( 35,176)( 36,177)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49, 97)( 50, 98)( 51, 99)( 52,100)( 53,101)( 54,102)( 55,103)( 56,104)
( 57,105)( 58,106)( 59,107)( 60,108)( 61,112)( 62,113)( 63,114)( 64,109)
( 65,110)( 66,111)( 67,118)( 68,119)( 69,120)( 70,115)( 71,116)( 72,117)
( 73,124)( 74,125)( 75,126)( 76,121)( 77,122)( 78,123)( 79,130)( 80,131)
( 81,132)( 82,127)( 83,128)( 84,129)( 85,133)( 86,134)( 87,135)( 88,136)
( 89,137)( 90,138)( 91,139)( 92,140)( 93,141)( 94,142)( 95,143)( 96,144)
(193,337)(194,338)(195,339)(196,340)(197,341)(198,342)(199,343)(200,344)
(201,345)(202,346)(203,347)(204,348)(205,352)(206,353)(207,354)(208,349)
(209,350)(210,351)(211,358)(212,359)(213,360)(214,355)(215,356)(216,357)
(217,364)(218,365)(219,366)(220,361)(221,362)(222,363)(223,370)(224,371)
(225,372)(226,367)(227,368)(228,369)(229,373)(230,374)(231,375)(232,376)
(233,377)(234,378)(235,379)(236,380)(237,381)(238,382)(239,383)(240,384)
(241,289)(242,290)(243,291)(244,292)(245,293)(246,294)(247,295)(248,296)
(249,297)(250,298)(251,299)(252,300)(253,304)(254,305)(255,306)(256,301)
(257,302)(258,303)(259,310)(260,311)(261,312)(262,307)(263,308)(264,309)
(265,316)(266,317)(267,318)(268,313)(269,314)(270,315)(271,322)(272,323)
(273,324)(274,319)(275,320)(276,321)(277,325)(278,326)(279,327)(280,328)
(281,329)(282,330)(283,331)(284,332)(285,333)(286,334)(287,335)(288,336);;
s3 := ( 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);;
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*s3*s2*s3*s2*s3*s2*s3,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*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, 49)( 2, 51)( 3, 50)( 4, 52)( 5, 54)( 6, 53)( 7, 55)
( 8, 57)( 9, 56)( 10, 58)( 11, 60)( 12, 59)( 13, 61)( 14, 63)( 15, 62)
( 16, 64)( 17, 66)( 18, 65)( 19, 67)( 20, 69)( 21, 68)( 22, 70)( 23, 72)
( 24, 71)( 25, 76)( 26, 78)( 27, 77)( 28, 73)( 29, 75)( 30, 74)( 31, 82)
( 32, 84)( 33, 83)( 34, 79)( 35, 81)( 36, 80)( 37, 88)( 38, 90)( 39, 89)
( 40, 85)( 41, 87)( 42, 86)( 43, 94)( 44, 96)( 45, 95)( 46, 91)( 47, 93)
( 48, 92)( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,151)
(104,153)(105,152)(106,154)(107,156)(108,155)(109,157)(110,159)(111,158)
(112,160)(113,162)(114,161)(115,163)(116,165)(117,164)(118,166)(119,168)
(120,167)(121,172)(122,174)(123,173)(124,169)(125,171)(126,170)(127,178)
(128,180)(129,179)(130,175)(131,177)(132,176)(133,184)(134,186)(135,185)
(136,181)(137,183)(138,182)(139,190)(140,192)(141,191)(142,187)(143,189)
(144,188)(193,241)(194,243)(195,242)(196,244)(197,246)(198,245)(199,247)
(200,249)(201,248)(202,250)(203,252)(204,251)(205,253)(206,255)(207,254)
(208,256)(209,258)(210,257)(211,259)(212,261)(213,260)(214,262)(215,264)
(216,263)(217,268)(218,270)(219,269)(220,265)(221,267)(222,266)(223,274)
(224,276)(225,275)(226,271)(227,273)(228,272)(229,280)(230,282)(231,281)
(232,277)(233,279)(234,278)(235,286)(236,288)(237,287)(238,283)(239,285)
(240,284)(289,337)(290,339)(291,338)(292,340)(293,342)(294,341)(295,343)
(296,345)(297,344)(298,346)(299,348)(300,347)(301,349)(302,351)(303,350)
(304,352)(305,354)(306,353)(307,355)(308,357)(309,356)(310,358)(311,360)
(312,359)(313,364)(314,366)(315,365)(316,361)(317,363)(318,362)(319,370)
(320,372)(321,371)(322,367)(323,369)(324,368)(325,376)(326,378)(327,377)
(328,373)(329,375)(330,374)(331,382)(332,384)(333,383)(334,379)(335,381)
(336,380);
s1 := 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);
s2 := Sym(384)!( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)
( 8,152)( 9,153)( 10,154)( 11,155)( 12,156)( 13,160)( 14,161)( 15,162)
( 16,157)( 17,158)( 18,159)( 19,166)( 20,167)( 21,168)( 22,163)( 23,164)
( 24,165)( 25,172)( 26,173)( 27,174)( 28,169)( 29,170)( 30,171)( 31,178)
( 32,179)( 33,180)( 34,175)( 35,176)( 36,177)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49, 97)( 50, 98)( 51, 99)( 52,100)( 53,101)( 54,102)( 55,103)
( 56,104)( 57,105)( 58,106)( 59,107)( 60,108)( 61,112)( 62,113)( 63,114)
( 64,109)( 65,110)( 66,111)( 67,118)( 68,119)( 69,120)( 70,115)( 71,116)
( 72,117)( 73,124)( 74,125)( 75,126)( 76,121)( 77,122)( 78,123)( 79,130)
( 80,131)( 81,132)( 82,127)( 83,128)( 84,129)( 85,133)( 86,134)( 87,135)
( 88,136)( 89,137)( 90,138)( 91,139)( 92,140)( 93,141)( 94,142)( 95,143)
( 96,144)(193,337)(194,338)(195,339)(196,340)(197,341)(198,342)(199,343)
(200,344)(201,345)(202,346)(203,347)(204,348)(205,352)(206,353)(207,354)
(208,349)(209,350)(210,351)(211,358)(212,359)(213,360)(214,355)(215,356)
(216,357)(217,364)(218,365)(219,366)(220,361)(221,362)(222,363)(223,370)
(224,371)(225,372)(226,367)(227,368)(228,369)(229,373)(230,374)(231,375)
(232,376)(233,377)(234,378)(235,379)(236,380)(237,381)(238,382)(239,383)
(240,384)(241,289)(242,290)(243,291)(244,292)(245,293)(246,294)(247,295)
(248,296)(249,297)(250,298)(251,299)(252,300)(253,304)(254,305)(255,306)
(256,301)(257,302)(258,303)(259,310)(260,311)(261,312)(262,307)(263,308)
(264,309)(265,316)(266,317)(267,318)(268,313)(269,314)(270,315)(271,322)
(272,323)(273,324)(274,319)(275,320)(276,321)(277,325)(278,326)(279,327)
(280,328)(281,329)(282,330)(283,331)(284,332)(285,333)(286,334)(287,335)
(288,336);
s3 := 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);
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*s3*s2*s3*s2*s3*s2*s3, s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope