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Polytope of Type {24,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4,4}*768a
Also Known As : {{24,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(768,200568)
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}*384a, {24,2,4}*384
   3-fold quotients : {8,4,4}*256a
   4-fold quotients : {12,4,2}*192a, {12,2,4}*192, {6,4,4}*192, {24,2,2}*192
   6-fold quotients : {4,4,4}*128, {8,4,2}*128a, {8,2,4}*128
   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, {8,2,2}*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, 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);;
s2 := (  1, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,103)(  8,104)
(  9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)( 16,112)
( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)( 24,120)
( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)
( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)( 48,144)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)
( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,159)( 64,160)
( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)( 72,168)
( 73,169)( 74,170)( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)( 80,176)
( 81,177)( 82,178)( 83,179)( 84,180)( 85,181)( 86,182)( 87,183)( 88,184)
( 89,185)( 90,186)( 91,187)( 92,188)( 93,189)( 94,190)( 95,191)( 96,192)
(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)(200,296)
(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)(208,304)
(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)(216,312)
(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)(224,320)
(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)(232,328)
(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)(240,336)
(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)(248,344)
(249,345)(250,346)(251,347)(252,348)(253,349)(254,350)(255,351)(256,352)
(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)
(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)(272,368)
(273,369)(274,370)(275,371)(276,372)(277,373)(278,374)(279,375)(280,376)
(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)(288,384);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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, 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, 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);
s2 := Sym(384)!(  1, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,103)
(  8,104)(  9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)
( 16,112)( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)
( 24,120)( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)
( 32,128)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)
( 40,136)( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)
( 48,144)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)
( 56,152)( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,159)
( 64,160)( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)
( 72,168)( 73,169)( 74,170)( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)
( 80,176)( 81,177)( 82,178)( 83,179)( 84,180)( 85,181)( 86,182)( 87,183)
( 88,184)( 89,185)( 90,186)( 91,187)( 92,188)( 93,189)( 94,190)( 95,191)
( 96,192)(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)
(200,296)(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)
(208,304)(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)
(216,312)(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)
(224,320)(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)
(232,328)(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)
(240,336)(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)
(248,344)(249,345)(250,346)(251,347)(252,348)(253,349)(254,350)(255,351)
(256,352)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)
(264,360)(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)
(272,368)(273,369)(274,370)(275,371)(276,372)(277,373)(278,374)(279,375)
(280,376)(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)
(288,384);
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, 
s0*s1*s2*s1*s0*s1*s2*s1, 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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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