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