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