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Polytope of Type {6,8,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,8}*768a
if this polytope has a name.
Group : SmallGroup(768,145169)
Rank : 4
Schlafli Type : {6,8,8}
Number of vertices, edges, etc : 6, 24, 32, 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 : {6,4,8}*384a, {6,8,4}*384b
   3-fold quotients : {2,8,8}*256a
   4-fold quotients : {6,4,4}*192, {6,2,8}*192
   6-fold quotients : {2,4,8}*128a, {2,8,4}*128b
   8-fold quotients : {3,2,8}*96, {6,2,4}*96, {6,4,2}*96a
   12-fold quotients : {2,4,4}*64, {2,2,8}*64
   16-fold quotients : {3,2,4}*48, {6,2,2}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*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, 73)( 26, 75)( 27, 74)( 28, 76)( 29, 78)( 30, 77)( 31, 79)( 32, 81)
( 33, 80)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 87)( 39, 86)( 40, 88)
( 41, 90)( 42, 89)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 96)( 48, 95)
( 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)
(121,169)(122,171)(123,170)(124,172)(125,174)(126,173)(127,175)(128,177)
(129,176)(130,178)(131,180)(132,179)(133,181)(134,183)(135,182)(136,184)
(137,186)(138,185)(139,187)(140,189)(141,188)(142,190)(143,192)(144,191)
(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)
(217,265)(218,267)(219,266)(220,268)(221,270)(222,269)(223,271)(224,273)
(225,272)(226,274)(227,276)(228,275)(229,277)(230,279)(231,278)(232,280)
(233,282)(234,281)(235,283)(236,285)(237,284)(238,286)(239,288)(240,287)
(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)
(313,361)(314,363)(315,362)(316,364)(317,366)(318,365)(319,367)(320,369)
(321,368)(322,370)(323,372)(324,371)(325,373)(326,375)(327,374)(328,376)
(329,378)(330,377)(331,379)(332,381)(333,380)(334,382)(335,384)(336,383);;
s1 := (  1,147)(  2,146)(  3,145)(  4,150)(  5,149)(  6,148)(  7,153)(  8,152)
(  9,151)( 10,156)( 11,155)( 12,154)( 13,162)( 14,161)( 15,160)( 16,159)
( 17,158)( 18,157)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)( 24,163)
( 25,174)( 26,173)( 27,172)( 28,171)( 29,170)( 30,169)( 31,180)( 32,179)
( 33,178)( 34,177)( 35,176)( 36,175)( 37,183)( 38,182)( 39,181)( 40,186)
( 41,185)( 42,184)( 43,189)( 44,188)( 45,187)( 46,192)( 47,191)( 48,190)
( 49, 99)( 50, 98)( 51, 97)( 52,102)( 53,101)( 54,100)( 55,105)( 56,104)
( 57,103)( 58,108)( 59,107)( 60,106)( 61,114)( 62,113)( 63,112)( 64,111)
( 65,110)( 66,109)( 67,120)( 68,119)( 69,118)( 70,117)( 71,116)( 72,115)
( 73,126)( 74,125)( 75,124)( 76,123)( 77,122)( 78,121)( 79,132)( 80,131)
( 81,130)( 82,129)( 83,128)( 84,127)( 85,135)( 86,134)( 87,133)( 88,138)
( 89,137)( 90,136)( 91,141)( 92,140)( 93,139)( 94,144)( 95,143)( 96,142)
(193,339)(194,338)(195,337)(196,342)(197,341)(198,340)(199,345)(200,344)
(201,343)(202,348)(203,347)(204,346)(205,354)(206,353)(207,352)(208,351)
(209,350)(210,349)(211,360)(212,359)(213,358)(214,357)(215,356)(216,355)
(217,366)(218,365)(219,364)(220,363)(221,362)(222,361)(223,372)(224,371)
(225,370)(226,369)(227,368)(228,367)(229,375)(230,374)(231,373)(232,378)
(233,377)(234,376)(235,381)(236,380)(237,379)(238,384)(239,383)(240,382)
(241,291)(242,290)(243,289)(244,294)(245,293)(246,292)(247,297)(248,296)
(249,295)(250,300)(251,299)(252,298)(253,306)(254,305)(255,304)(256,303)
(257,302)(258,301)(259,312)(260,311)(261,310)(262,309)(263,308)(264,307)
(265,318)(266,317)(267,316)(268,315)(269,314)(270,313)(271,324)(272,323)
(273,322)(274,321)(275,320)(276,319)(277,327)(278,326)(279,325)(280,330)
(281,329)(282,328)(283,333)(284,332)(285,331)(286,336)(287,335)(288,334);;
s2 := ( 13, 16)( 14, 17)( 15, 18)( 19, 22)( 20, 23)( 21, 24)( 25, 31)( 26, 32)
( 27, 33)( 28, 34)( 29, 35)( 30, 36)( 37, 46)( 38, 47)( 39, 48)( 40, 43)
( 41, 44)( 42, 45)( 61, 64)( 62, 65)( 63, 66)( 67, 70)( 68, 71)( 69, 72)
( 73, 79)( 74, 80)( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 85, 94)( 86, 95)
( 87, 96)( 88, 91)( 89, 92)( 90, 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)
(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(127,133)(128,134)
(129,135)(130,136)(131,137)(132,138)(145,157)(146,158)(147,159)(148,160)
(149,161)(150,162)(151,163)(152,164)(153,165)(154,166)(155,167)(156,168)
(169,187)(170,188)(171,189)(172,190)(173,191)(174,192)(175,181)(176,182)
(177,183)(178,184)(179,185)(180,186)(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)(241,265)(242,266)(243,267)(244,268)
(245,269)(246,270)(247,271)(248,272)(249,273)(250,274)(251,275)(252,276)
(253,280)(254,281)(255,282)(256,277)(257,278)(258,279)(259,286)(260,287)
(261,288)(262,283)(263,284)(264,285)(289,328)(290,329)(291,330)(292,325)
(293,326)(294,327)(295,334)(296,335)(297,336)(298,331)(299,332)(300,333)
(301,316)(302,317)(303,318)(304,313)(305,314)(306,315)(307,322)(308,323)
(309,324)(310,319)(311,320)(312,321)(337,376)(338,377)(339,378)(340,373)
(341,374)(342,375)(343,382)(344,383)(345,384)(346,379)(347,380)(348,381)
(349,364)(350,365)(351,366)(352,361)(353,362)(354,363)(355,370)(356,371)
(357,372)(358,367)(359,368)(360,369);;
s3 := (  1,193)(  2,194)(  3,195)(  4,196)(  5,197)(  6,198)(  7,199)(  8,200)
(  9,201)( 10,202)( 11,203)( 12,204)( 13,208)( 14,209)( 15,210)( 16,205)
( 17,206)( 18,207)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)( 24,213)
( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,217)( 32,218)
( 33,219)( 34,220)( 35,221)( 36,222)( 37,238)( 38,239)( 39,240)( 40,235)
( 41,236)( 42,237)( 43,232)( 44,233)( 45,234)( 46,229)( 47,230)( 48,231)
( 49,241)( 50,242)( 51,243)( 52,244)( 53,245)( 54,246)( 55,247)( 56,248)
( 57,249)( 58,250)( 59,251)( 60,252)( 61,256)( 62,257)( 63,258)( 64,253)
( 65,254)( 66,255)( 67,262)( 68,263)( 69,264)( 70,259)( 71,260)( 72,261)
( 73,271)( 74,272)( 75,273)( 76,274)( 77,275)( 78,276)( 79,265)( 80,266)
( 81,267)( 82,268)( 83,269)( 84,270)( 85,286)( 86,287)( 87,288)( 88,283)
( 89,284)( 90,285)( 91,280)( 92,281)( 93,282)( 94,277)( 95,278)( 96,279)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,295)(104,296)
(105,297)(106,298)(107,299)(108,300)(109,304)(110,305)(111,306)(112,301)
(113,302)(114,303)(115,310)(116,311)(117,312)(118,307)(119,308)(120,309)
(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,313)(128,314)
(129,315)(130,316)(131,317)(132,318)(133,334)(134,335)(135,336)(136,331)
(137,332)(138,333)(139,328)(140,329)(141,330)(142,325)(143,326)(144,327)
(145,337)(146,338)(147,339)(148,340)(149,341)(150,342)(151,343)(152,344)
(153,345)(154,346)(155,347)(156,348)(157,352)(158,353)(159,354)(160,349)
(161,350)(162,351)(163,358)(164,359)(165,360)(166,355)(167,356)(168,357)
(169,367)(170,368)(171,369)(172,370)(173,371)(174,372)(175,361)(176,362)
(177,363)(178,364)(179,365)(180,366)(181,382)(182,383)(183,384)(184,379)
(185,380)(186,381)(187,376)(188,377)(189,378)(190,373)(191,374)(192,375);;
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, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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, 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, 73)( 26, 75)( 27, 74)( 28, 76)( 29, 78)( 30, 77)( 31, 79)
( 32, 81)( 33, 80)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 87)( 39, 86)
( 40, 88)( 41, 90)( 42, 89)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 96)
( 48, 95)( 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)(121,169)(122,171)(123,170)(124,172)(125,174)(126,173)(127,175)
(128,177)(129,176)(130,178)(131,180)(132,179)(133,181)(134,183)(135,182)
(136,184)(137,186)(138,185)(139,187)(140,189)(141,188)(142,190)(143,192)
(144,191)(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)(217,265)(218,267)(219,266)(220,268)(221,270)(222,269)(223,271)
(224,273)(225,272)(226,274)(227,276)(228,275)(229,277)(230,279)(231,278)
(232,280)(233,282)(234,281)(235,283)(236,285)(237,284)(238,286)(239,288)
(240,287)(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)(313,361)(314,363)(315,362)(316,364)(317,366)(318,365)(319,367)
(320,369)(321,368)(322,370)(323,372)(324,371)(325,373)(326,375)(327,374)
(328,376)(329,378)(330,377)(331,379)(332,381)(333,380)(334,382)(335,384)
(336,383);
s1 := Sym(384)!(  1,147)(  2,146)(  3,145)(  4,150)(  5,149)(  6,148)(  7,153)
(  8,152)(  9,151)( 10,156)( 11,155)( 12,154)( 13,162)( 14,161)( 15,160)
( 16,159)( 17,158)( 18,157)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)
( 24,163)( 25,174)( 26,173)( 27,172)( 28,171)( 29,170)( 30,169)( 31,180)
( 32,179)( 33,178)( 34,177)( 35,176)( 36,175)( 37,183)( 38,182)( 39,181)
( 40,186)( 41,185)( 42,184)( 43,189)( 44,188)( 45,187)( 46,192)( 47,191)
( 48,190)( 49, 99)( 50, 98)( 51, 97)( 52,102)( 53,101)( 54,100)( 55,105)
( 56,104)( 57,103)( 58,108)( 59,107)( 60,106)( 61,114)( 62,113)( 63,112)
( 64,111)( 65,110)( 66,109)( 67,120)( 68,119)( 69,118)( 70,117)( 71,116)
( 72,115)( 73,126)( 74,125)( 75,124)( 76,123)( 77,122)( 78,121)( 79,132)
( 80,131)( 81,130)( 82,129)( 83,128)( 84,127)( 85,135)( 86,134)( 87,133)
( 88,138)( 89,137)( 90,136)( 91,141)( 92,140)( 93,139)( 94,144)( 95,143)
( 96,142)(193,339)(194,338)(195,337)(196,342)(197,341)(198,340)(199,345)
(200,344)(201,343)(202,348)(203,347)(204,346)(205,354)(206,353)(207,352)
(208,351)(209,350)(210,349)(211,360)(212,359)(213,358)(214,357)(215,356)
(216,355)(217,366)(218,365)(219,364)(220,363)(221,362)(222,361)(223,372)
(224,371)(225,370)(226,369)(227,368)(228,367)(229,375)(230,374)(231,373)
(232,378)(233,377)(234,376)(235,381)(236,380)(237,379)(238,384)(239,383)
(240,382)(241,291)(242,290)(243,289)(244,294)(245,293)(246,292)(247,297)
(248,296)(249,295)(250,300)(251,299)(252,298)(253,306)(254,305)(255,304)
(256,303)(257,302)(258,301)(259,312)(260,311)(261,310)(262,309)(263,308)
(264,307)(265,318)(266,317)(267,316)(268,315)(269,314)(270,313)(271,324)
(272,323)(273,322)(274,321)(275,320)(276,319)(277,327)(278,326)(279,325)
(280,330)(281,329)(282,328)(283,333)(284,332)(285,331)(286,336)(287,335)
(288,334);
s2 := Sym(384)!( 13, 16)( 14, 17)( 15, 18)( 19, 22)( 20, 23)( 21, 24)( 25, 31)
( 26, 32)( 27, 33)( 28, 34)( 29, 35)( 30, 36)( 37, 46)( 38, 47)( 39, 48)
( 40, 43)( 41, 44)( 42, 45)( 61, 64)( 62, 65)( 63, 66)( 67, 70)( 68, 71)
( 69, 72)( 73, 79)( 74, 80)( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 85, 94)
( 86, 95)( 87, 96)( 88, 91)( 89, 92)( 90, 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)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(127,133)
(128,134)(129,135)(130,136)(131,137)(132,138)(145,157)(146,158)(147,159)
(148,160)(149,161)(150,162)(151,163)(152,164)(153,165)(154,166)(155,167)
(156,168)(169,187)(170,188)(171,189)(172,190)(173,191)(174,192)(175,181)
(176,182)(177,183)(178,184)(179,185)(180,186)(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)(241,265)(242,266)(243,267)
(244,268)(245,269)(246,270)(247,271)(248,272)(249,273)(250,274)(251,275)
(252,276)(253,280)(254,281)(255,282)(256,277)(257,278)(258,279)(259,286)
(260,287)(261,288)(262,283)(263,284)(264,285)(289,328)(290,329)(291,330)
(292,325)(293,326)(294,327)(295,334)(296,335)(297,336)(298,331)(299,332)
(300,333)(301,316)(302,317)(303,318)(304,313)(305,314)(306,315)(307,322)
(308,323)(309,324)(310,319)(311,320)(312,321)(337,376)(338,377)(339,378)
(340,373)(341,374)(342,375)(343,382)(344,383)(345,384)(346,379)(347,380)
(348,381)(349,364)(350,365)(351,366)(352,361)(353,362)(354,363)(355,370)
(356,371)(357,372)(358,367)(359,368)(360,369);
s3 := Sym(384)!(  1,193)(  2,194)(  3,195)(  4,196)(  5,197)(  6,198)(  7,199)
(  8,200)(  9,201)( 10,202)( 11,203)( 12,204)( 13,208)( 14,209)( 15,210)
( 16,205)( 17,206)( 18,207)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)
( 24,213)( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,217)
( 32,218)( 33,219)( 34,220)( 35,221)( 36,222)( 37,238)( 38,239)( 39,240)
( 40,235)( 41,236)( 42,237)( 43,232)( 44,233)( 45,234)( 46,229)( 47,230)
( 48,231)( 49,241)( 50,242)( 51,243)( 52,244)( 53,245)( 54,246)( 55,247)
( 56,248)( 57,249)( 58,250)( 59,251)( 60,252)( 61,256)( 62,257)( 63,258)
( 64,253)( 65,254)( 66,255)( 67,262)( 68,263)( 69,264)( 70,259)( 71,260)
( 72,261)( 73,271)( 74,272)( 75,273)( 76,274)( 77,275)( 78,276)( 79,265)
( 80,266)( 81,267)( 82,268)( 83,269)( 84,270)( 85,286)( 86,287)( 87,288)
( 88,283)( 89,284)( 90,285)( 91,280)( 92,281)( 93,282)( 94,277)( 95,278)
( 96,279)( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,295)
(104,296)(105,297)(106,298)(107,299)(108,300)(109,304)(110,305)(111,306)
(112,301)(113,302)(114,303)(115,310)(116,311)(117,312)(118,307)(119,308)
(120,309)(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,313)
(128,314)(129,315)(130,316)(131,317)(132,318)(133,334)(134,335)(135,336)
(136,331)(137,332)(138,333)(139,328)(140,329)(141,330)(142,325)(143,326)
(144,327)(145,337)(146,338)(147,339)(148,340)(149,341)(150,342)(151,343)
(152,344)(153,345)(154,346)(155,347)(156,348)(157,352)(158,353)(159,354)
(160,349)(161,350)(162,351)(163,358)(164,359)(165,360)(166,355)(167,356)
(168,357)(169,367)(170,368)(171,369)(172,370)(173,371)(174,372)(175,361)
(176,362)(177,363)(178,364)(179,365)(180,366)(181,382)(182,383)(183,384)
(184,379)(185,380)(186,381)(187,376)(188,377)(189,378)(190,373)(191,374)
(192,375);
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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope