Polytope of Type {4,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,6}*768c
if this polytope has a name.
Group : SmallGroup(768,1088539)
Rank : 4
Schlafli Type : {4,4,6}
Number of vertices, edges, etc : 16, 32, 48, 6
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 4
Special Properties :
   Universal
   Non-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 : {4,4,3}*384a, {4,4,6}*384b
   4-fold quotients : {4,4,3}*192a
   8-fold quotients : {2,4,6}*96c
   16-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,103)(  8,104)
(  9,108)( 10,107)( 11,106)( 12,105)( 13,112)( 14,111)( 15,110)( 16,109)
( 17,118)( 18,117)( 19,120)( 20,119)( 21,114)( 22,113)( 23,116)( 24,115)
( 25,128)( 26,127)( 27,126)( 28,125)( 29,124)( 30,123)( 31,122)( 32,121)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)
( 41,140)( 42,139)( 43,138)( 44,137)( 45,144)( 46,143)( 47,142)( 48,141)
( 49,150)( 50,149)( 51,152)( 52,151)( 53,146)( 54,145)( 55,148)( 56,147)
( 57,160)( 58,159)( 59,158)( 60,157)( 61,156)( 62,155)( 63,154)( 64,153)
( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)( 72,168)
( 73,172)( 74,171)( 75,170)( 76,169)( 77,176)( 78,175)( 79,174)( 80,173)
( 81,182)( 82,181)( 83,184)( 84,183)( 85,178)( 86,177)( 87,180)( 88,179)
( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,187)( 95,186)( 96,185)
(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)(200,296)
(201,300)(202,299)(203,298)(204,297)(205,304)(206,303)(207,302)(208,301)
(209,310)(210,309)(211,312)(212,311)(213,306)(214,305)(215,308)(216,307)
(217,320)(218,319)(219,318)(220,317)(221,316)(222,315)(223,314)(224,313)
(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)(232,328)
(233,332)(234,331)(235,330)(236,329)(237,336)(238,335)(239,334)(240,333)
(241,342)(242,341)(243,344)(244,343)(245,338)(246,337)(247,340)(248,339)
(249,352)(250,351)(251,350)(252,349)(253,348)(254,347)(255,346)(256,345)
(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)
(265,364)(266,363)(267,362)(268,361)(269,368)(270,367)(271,366)(272,365)
(273,374)(274,373)(275,376)(276,375)(277,370)(278,369)(279,372)(280,371)
(281,384)(282,383)(283,382)(284,381)(285,380)(286,379)(287,378)(288,377);;
s1 := (  1, 25)(  2, 26)(  3, 28)(  4, 27)(  5, 30)(  6, 29)(  7, 31)(  8, 32)
(  9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 22)( 14, 21)( 15, 23)( 16, 24)
( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 62)( 38, 61)( 39, 63)( 40, 64)
( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 45, 54)( 46, 53)( 47, 55)( 48, 56)
( 65, 89)( 66, 90)( 67, 92)( 68, 91)( 69, 94)( 70, 93)( 71, 95)( 72, 96)
( 73, 81)( 74, 82)( 75, 84)( 76, 83)( 77, 86)( 78, 85)( 79, 87)( 80, 88)
( 97,121)( 98,122)( 99,124)(100,123)(101,126)(102,125)(103,127)(104,128)
(105,113)(106,114)(107,116)(108,115)(109,118)(110,117)(111,119)(112,120)
(129,153)(130,154)(131,156)(132,155)(133,158)(134,157)(135,159)(136,160)
(137,145)(138,146)(139,148)(140,147)(141,150)(142,149)(143,151)(144,152)
(161,185)(162,186)(163,188)(164,187)(165,190)(166,189)(167,191)(168,192)
(169,177)(170,178)(171,180)(172,179)(173,182)(174,181)(175,183)(176,184)
(193,217)(194,218)(195,220)(196,219)(197,222)(198,221)(199,223)(200,224)
(201,209)(202,210)(203,212)(204,211)(205,214)(206,213)(207,215)(208,216)
(225,249)(226,250)(227,252)(228,251)(229,254)(230,253)(231,255)(232,256)
(233,241)(234,242)(235,244)(236,243)(237,246)(238,245)(239,247)(240,248)
(257,281)(258,282)(259,284)(260,283)(261,286)(262,285)(263,287)(264,288)
(265,273)(266,274)(267,276)(268,275)(269,278)(270,277)(271,279)(272,280)
(289,313)(290,314)(291,316)(292,315)(293,318)(294,317)(295,319)(296,320)
(297,305)(298,306)(299,308)(300,307)(301,310)(302,309)(303,311)(304,312)
(321,345)(322,346)(323,348)(324,347)(325,350)(326,349)(327,351)(328,352)
(329,337)(330,338)(331,340)(332,339)(333,342)(334,341)(335,343)(336,344)
(353,377)(354,378)(355,380)(356,379)(357,382)(358,381)(359,383)(360,384)
(361,369)(362,370)(363,372)(364,371)(365,374)(366,373)(367,375)(368,376);;
s2 := (  5,  7)(  6,  8)( 13, 15)( 14, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)
( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)( 34, 66)( 35, 67)( 36, 68)
( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)( 42, 74)( 43, 75)( 44, 76)
( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)( 50, 90)( 51, 91)( 52, 92)
( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)( 59, 83)( 60, 84)
( 61, 87)( 62, 88)( 63, 85)( 64, 86)(101,103)(102,104)(109,111)(110,112)
(113,121)(114,122)(115,123)(116,124)(117,127)(118,128)(119,125)(120,126)
(129,161)(130,162)(131,163)(132,164)(133,167)(134,168)(135,165)(136,166)
(137,169)(138,170)(139,171)(140,172)(141,175)(142,176)(143,173)(144,174)
(145,185)(146,186)(147,187)(148,188)(149,191)(150,192)(151,189)(152,190)
(153,177)(154,178)(155,179)(156,180)(157,183)(158,184)(159,181)(160,182)
(197,199)(198,200)(205,207)(206,208)(209,217)(210,218)(211,219)(212,220)
(213,223)(214,224)(215,221)(216,222)(225,257)(226,258)(227,259)(228,260)
(229,263)(230,264)(231,261)(232,262)(233,265)(234,266)(235,267)(236,268)
(237,271)(238,272)(239,269)(240,270)(241,281)(242,282)(243,283)(244,284)
(245,287)(246,288)(247,285)(248,286)(249,273)(250,274)(251,275)(252,276)
(253,279)(254,280)(255,277)(256,278)(293,295)(294,296)(301,303)(302,304)
(305,313)(306,314)(307,315)(308,316)(309,319)(310,320)(311,317)(312,318)
(321,353)(322,354)(323,355)(324,356)(325,359)(326,360)(327,357)(328,358)
(329,361)(330,362)(331,363)(332,364)(333,367)(334,368)(335,365)(336,366)
(337,377)(338,378)(339,379)(340,380)(341,383)(342,384)(343,381)(344,382)
(345,369)(346,370)(347,371)(348,372)(349,375)(350,376)(351,373)(352,374);;
s3 := (  1,257)(  2,258)(  3,261)(  4,262)(  5,259)(  6,260)(  7,263)(  8,264)
(  9,273)( 10,274)( 11,277)( 12,278)( 13,275)( 14,276)( 15,279)( 16,280)
( 17,265)( 18,266)( 19,269)( 20,270)( 21,267)( 22,268)( 23,271)( 24,272)
( 25,281)( 26,282)( 27,285)( 28,286)( 29,283)( 30,284)( 31,287)( 32,288)
( 33,225)( 34,226)( 35,229)( 36,230)( 37,227)( 38,228)( 39,231)( 40,232)
( 41,241)( 42,242)( 43,245)( 44,246)( 45,243)( 46,244)( 47,247)( 48,248)
( 49,233)( 50,234)( 51,237)( 52,238)( 53,235)( 54,236)( 55,239)( 56,240)
( 57,249)( 58,250)( 59,253)( 60,254)( 61,251)( 62,252)( 63,255)( 64,256)
( 65,193)( 66,194)( 67,197)( 68,198)( 69,195)( 70,196)( 71,199)( 72,200)
( 73,209)( 74,210)( 75,213)( 76,214)( 77,211)( 78,212)( 79,215)( 80,216)
( 81,201)( 82,202)( 83,205)( 84,206)( 85,203)( 86,204)( 87,207)( 88,208)
( 89,217)( 90,218)( 91,221)( 92,222)( 93,219)( 94,220)( 95,223)( 96,224)
( 97,353)( 98,354)( 99,357)(100,358)(101,355)(102,356)(103,359)(104,360)
(105,369)(106,370)(107,373)(108,374)(109,371)(110,372)(111,375)(112,376)
(113,361)(114,362)(115,365)(116,366)(117,363)(118,364)(119,367)(120,368)
(121,377)(122,378)(123,381)(124,382)(125,379)(126,380)(127,383)(128,384)
(129,321)(130,322)(131,325)(132,326)(133,323)(134,324)(135,327)(136,328)
(137,337)(138,338)(139,341)(140,342)(141,339)(142,340)(143,343)(144,344)
(145,329)(146,330)(147,333)(148,334)(149,331)(150,332)(151,335)(152,336)
(153,345)(154,346)(155,349)(156,350)(157,347)(158,348)(159,351)(160,352)
(161,289)(162,290)(163,293)(164,294)(165,291)(166,292)(167,295)(168,296)
(169,305)(170,306)(171,309)(172,310)(173,307)(174,308)(175,311)(176,312)
(177,297)(178,298)(179,301)(180,302)(181,299)(182,300)(183,303)(184,304)
(185,313)(186,314)(187,317)(188,318)(189,315)(190,316)(191,319)(192,320);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(384)!(  1, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,103)
(  8,104)(  9,108)( 10,107)( 11,106)( 12,105)( 13,112)( 14,111)( 15,110)
( 16,109)( 17,118)( 18,117)( 19,120)( 20,119)( 21,114)( 22,113)( 23,116)
( 24,115)( 25,128)( 26,127)( 27,126)( 28,125)( 29,124)( 30,123)( 31,122)
( 32,121)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)
( 40,136)( 41,140)( 42,139)( 43,138)( 44,137)( 45,144)( 46,143)( 47,142)
( 48,141)( 49,150)( 50,149)( 51,152)( 52,151)( 53,146)( 54,145)( 55,148)
( 56,147)( 57,160)( 58,159)( 59,158)( 60,157)( 61,156)( 62,155)( 63,154)
( 64,153)( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)
( 72,168)( 73,172)( 74,171)( 75,170)( 76,169)( 77,176)( 78,175)( 79,174)
( 80,173)( 81,182)( 82,181)( 83,184)( 84,183)( 85,178)( 86,177)( 87,180)
( 88,179)( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,187)( 95,186)
( 96,185)(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)
(200,296)(201,300)(202,299)(203,298)(204,297)(205,304)(206,303)(207,302)
(208,301)(209,310)(210,309)(211,312)(212,311)(213,306)(214,305)(215,308)
(216,307)(217,320)(218,319)(219,318)(220,317)(221,316)(222,315)(223,314)
(224,313)(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)
(232,328)(233,332)(234,331)(235,330)(236,329)(237,336)(238,335)(239,334)
(240,333)(241,342)(242,341)(243,344)(244,343)(245,338)(246,337)(247,340)
(248,339)(249,352)(250,351)(251,350)(252,349)(253,348)(254,347)(255,346)
(256,345)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)
(264,360)(265,364)(266,363)(267,362)(268,361)(269,368)(270,367)(271,366)
(272,365)(273,374)(274,373)(275,376)(276,375)(277,370)(278,369)(279,372)
(280,371)(281,384)(282,383)(283,382)(284,381)(285,380)(286,379)(287,378)
(288,377);
s1 := Sym(384)!(  1, 25)(  2, 26)(  3, 28)(  4, 27)(  5, 30)(  6, 29)(  7, 31)
(  8, 32)(  9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 22)( 14, 21)( 15, 23)
( 16, 24)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 62)( 38, 61)( 39, 63)
( 40, 64)( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 45, 54)( 46, 53)( 47, 55)
( 48, 56)( 65, 89)( 66, 90)( 67, 92)( 68, 91)( 69, 94)( 70, 93)( 71, 95)
( 72, 96)( 73, 81)( 74, 82)( 75, 84)( 76, 83)( 77, 86)( 78, 85)( 79, 87)
( 80, 88)( 97,121)( 98,122)( 99,124)(100,123)(101,126)(102,125)(103,127)
(104,128)(105,113)(106,114)(107,116)(108,115)(109,118)(110,117)(111,119)
(112,120)(129,153)(130,154)(131,156)(132,155)(133,158)(134,157)(135,159)
(136,160)(137,145)(138,146)(139,148)(140,147)(141,150)(142,149)(143,151)
(144,152)(161,185)(162,186)(163,188)(164,187)(165,190)(166,189)(167,191)
(168,192)(169,177)(170,178)(171,180)(172,179)(173,182)(174,181)(175,183)
(176,184)(193,217)(194,218)(195,220)(196,219)(197,222)(198,221)(199,223)
(200,224)(201,209)(202,210)(203,212)(204,211)(205,214)(206,213)(207,215)
(208,216)(225,249)(226,250)(227,252)(228,251)(229,254)(230,253)(231,255)
(232,256)(233,241)(234,242)(235,244)(236,243)(237,246)(238,245)(239,247)
(240,248)(257,281)(258,282)(259,284)(260,283)(261,286)(262,285)(263,287)
(264,288)(265,273)(266,274)(267,276)(268,275)(269,278)(270,277)(271,279)
(272,280)(289,313)(290,314)(291,316)(292,315)(293,318)(294,317)(295,319)
(296,320)(297,305)(298,306)(299,308)(300,307)(301,310)(302,309)(303,311)
(304,312)(321,345)(322,346)(323,348)(324,347)(325,350)(326,349)(327,351)
(328,352)(329,337)(330,338)(331,340)(332,339)(333,342)(334,341)(335,343)
(336,344)(353,377)(354,378)(355,380)(356,379)(357,382)(358,381)(359,383)
(360,384)(361,369)(362,370)(363,372)(364,371)(365,374)(366,373)(367,375)
(368,376);
s2 := Sym(384)!(  5,  7)(  6,  8)( 13, 15)( 14, 16)( 17, 25)( 18, 26)( 19, 27)
( 20, 28)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)( 34, 66)( 35, 67)
( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)( 42, 74)( 43, 75)
( 44, 76)( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)( 50, 90)( 51, 91)
( 52, 92)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)( 59, 83)
( 60, 84)( 61, 87)( 62, 88)( 63, 85)( 64, 86)(101,103)(102,104)(109,111)
(110,112)(113,121)(114,122)(115,123)(116,124)(117,127)(118,128)(119,125)
(120,126)(129,161)(130,162)(131,163)(132,164)(133,167)(134,168)(135,165)
(136,166)(137,169)(138,170)(139,171)(140,172)(141,175)(142,176)(143,173)
(144,174)(145,185)(146,186)(147,187)(148,188)(149,191)(150,192)(151,189)
(152,190)(153,177)(154,178)(155,179)(156,180)(157,183)(158,184)(159,181)
(160,182)(197,199)(198,200)(205,207)(206,208)(209,217)(210,218)(211,219)
(212,220)(213,223)(214,224)(215,221)(216,222)(225,257)(226,258)(227,259)
(228,260)(229,263)(230,264)(231,261)(232,262)(233,265)(234,266)(235,267)
(236,268)(237,271)(238,272)(239,269)(240,270)(241,281)(242,282)(243,283)
(244,284)(245,287)(246,288)(247,285)(248,286)(249,273)(250,274)(251,275)
(252,276)(253,279)(254,280)(255,277)(256,278)(293,295)(294,296)(301,303)
(302,304)(305,313)(306,314)(307,315)(308,316)(309,319)(310,320)(311,317)
(312,318)(321,353)(322,354)(323,355)(324,356)(325,359)(326,360)(327,357)
(328,358)(329,361)(330,362)(331,363)(332,364)(333,367)(334,368)(335,365)
(336,366)(337,377)(338,378)(339,379)(340,380)(341,383)(342,384)(343,381)
(344,382)(345,369)(346,370)(347,371)(348,372)(349,375)(350,376)(351,373)
(352,374);
s3 := Sym(384)!(  1,257)(  2,258)(  3,261)(  4,262)(  5,259)(  6,260)(  7,263)
(  8,264)(  9,273)( 10,274)( 11,277)( 12,278)( 13,275)( 14,276)( 15,279)
( 16,280)( 17,265)( 18,266)( 19,269)( 20,270)( 21,267)( 22,268)( 23,271)
( 24,272)( 25,281)( 26,282)( 27,285)( 28,286)( 29,283)( 30,284)( 31,287)
( 32,288)( 33,225)( 34,226)( 35,229)( 36,230)( 37,227)( 38,228)( 39,231)
( 40,232)( 41,241)( 42,242)( 43,245)( 44,246)( 45,243)( 46,244)( 47,247)
( 48,248)( 49,233)( 50,234)( 51,237)( 52,238)( 53,235)( 54,236)( 55,239)
( 56,240)( 57,249)( 58,250)( 59,253)( 60,254)( 61,251)( 62,252)( 63,255)
( 64,256)( 65,193)( 66,194)( 67,197)( 68,198)( 69,195)( 70,196)( 71,199)
( 72,200)( 73,209)( 74,210)( 75,213)( 76,214)( 77,211)( 78,212)( 79,215)
( 80,216)( 81,201)( 82,202)( 83,205)( 84,206)( 85,203)( 86,204)( 87,207)
( 88,208)( 89,217)( 90,218)( 91,221)( 92,222)( 93,219)( 94,220)( 95,223)
( 96,224)( 97,353)( 98,354)( 99,357)(100,358)(101,355)(102,356)(103,359)
(104,360)(105,369)(106,370)(107,373)(108,374)(109,371)(110,372)(111,375)
(112,376)(113,361)(114,362)(115,365)(116,366)(117,363)(118,364)(119,367)
(120,368)(121,377)(122,378)(123,381)(124,382)(125,379)(126,380)(127,383)
(128,384)(129,321)(130,322)(131,325)(132,326)(133,323)(134,324)(135,327)
(136,328)(137,337)(138,338)(139,341)(140,342)(141,339)(142,340)(143,343)
(144,344)(145,329)(146,330)(147,333)(148,334)(149,331)(150,332)(151,335)
(152,336)(153,345)(154,346)(155,349)(156,350)(157,347)(158,348)(159,351)
(160,352)(161,289)(162,290)(163,293)(164,294)(165,291)(166,292)(167,295)
(168,296)(169,305)(170,306)(171,309)(172,310)(173,307)(174,308)(175,311)
(176,312)(177,297)(178,298)(179,301)(180,302)(181,299)(182,300)(183,303)
(184,304)(185,313)(186,314)(187,317)(188,318)(189,315)(190,316)(191,319)
(192,320);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope