Polytope of Type {4,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6}*768d
if this polytope has a name.
Group : SmallGroup(768,1089108)
Rank : 4
Schlafli Type : {4,6,6}
Number of vertices, edges, etc : 8, 32, 48, 8
Order of s0s1s2s3 : 4
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}*384b, {4,6,3}*384b
4-fold quotients : {4,3,3}*192, {2,6,6}*192
8-fold quotients : {2,3,6}*96, {2,6,3}*96
16-fold quotients : {2,3,3}*48
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 49)( 2, 50)( 3, 51)( 4, 52)( 5, 54)( 6, 53)( 7, 56)( 8, 55)
( 9, 59)( 10, 60)( 11, 57)( 12, 58)( 13, 64)( 14, 63)( 15, 62)( 16, 61)
( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 70)( 22, 69)( 23, 72)( 24, 71)
( 25, 75)( 26, 76)( 27, 73)( 28, 74)( 29, 80)( 30, 79)( 31, 78)( 32, 77)
( 33, 81)( 34, 82)( 35, 83)( 36, 84)( 37, 86)( 38, 85)( 39, 88)( 40, 87)
( 41, 91)( 42, 92)( 43, 89)( 44, 90)( 45, 96)( 46, 95)( 47, 94)( 48, 93)
( 97,145)( 98,146)( 99,147)(100,148)(101,150)(102,149)(103,152)(104,151)
(105,155)(106,156)(107,153)(108,154)(109,160)(110,159)(111,158)(112,157)
(113,161)(114,162)(115,163)(116,164)(117,166)(118,165)(119,168)(120,167)
(121,171)(122,172)(123,169)(124,170)(125,176)(126,175)(127,174)(128,173)
(129,177)(130,178)(131,179)(132,180)(133,182)(134,181)(135,184)(136,183)
(137,187)(138,188)(139,185)(140,186)(141,192)(142,191)(143,190)(144,189)
(193,241)(194,242)(195,243)(196,244)(197,246)(198,245)(199,248)(200,247)
(201,251)(202,252)(203,249)(204,250)(205,256)(206,255)(207,254)(208,253)
(209,257)(210,258)(211,259)(212,260)(213,262)(214,261)(215,264)(216,263)
(217,267)(218,268)(219,265)(220,266)(221,272)(222,271)(223,270)(224,269)
(225,273)(226,274)(227,275)(228,276)(229,278)(230,277)(231,280)(232,279)
(233,283)(234,284)(235,281)(236,282)(237,288)(238,287)(239,286)(240,285)
(289,337)(290,338)(291,339)(292,340)(293,342)(294,341)(295,344)(296,343)
(297,347)(298,348)(299,345)(300,346)(301,352)(302,351)(303,350)(304,349)
(305,353)(306,354)(307,355)(308,356)(309,358)(310,357)(311,360)(312,359)
(313,363)(314,364)(315,361)(316,362)(317,368)(318,367)(319,366)(320,365)
(321,369)(322,370)(323,371)(324,372)(325,374)(326,373)(327,376)(328,375)
(329,379)(330,380)(331,377)(332,378)(333,384)(334,383)(335,382)(336,381);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 15, 16)( 17, 37)( 18, 38)
( 19, 40)( 20, 39)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 25, 41)( 26, 42)
( 27, 44)( 28, 43)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 49, 53)( 50, 54)
( 51, 56)( 52, 55)( 59, 60)( 63, 64)( 65, 85)( 66, 86)( 67, 88)( 68, 87)
( 69, 81)( 70, 82)( 71, 84)( 72, 83)( 73, 89)( 74, 90)( 75, 92)( 76, 91)
( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 97,101)( 98,102)( 99,104)(100,103)
(107,108)(111,112)(113,133)(114,134)(115,136)(116,135)(117,129)(118,130)
(119,132)(120,131)(121,137)(122,138)(123,140)(124,139)(125,141)(126,142)
(127,144)(128,143)(145,149)(146,150)(147,152)(148,151)(155,156)(159,160)
(161,181)(162,182)(163,184)(164,183)(165,177)(166,178)(167,180)(168,179)
(169,185)(170,186)(171,188)(172,187)(173,189)(174,190)(175,192)(176,191)
(193,197)(194,198)(195,200)(196,199)(203,204)(207,208)(209,229)(210,230)
(211,232)(212,231)(213,225)(214,226)(215,228)(216,227)(217,233)(218,234)
(219,236)(220,235)(221,237)(222,238)(223,240)(224,239)(241,245)(242,246)
(243,248)(244,247)(251,252)(255,256)(257,277)(258,278)(259,280)(260,279)
(261,273)(262,274)(263,276)(264,275)(265,281)(266,282)(267,284)(268,283)
(269,285)(270,286)(271,288)(272,287)(289,293)(290,294)(291,296)(292,295)
(299,300)(303,304)(305,325)(306,326)(307,328)(308,327)(309,321)(310,322)
(311,324)(312,323)(313,329)(314,330)(315,332)(316,331)(317,333)(318,334)
(319,336)(320,335)(337,341)(338,342)(339,344)(340,343)(347,348)(351,352)
(353,373)(354,374)(355,376)(356,375)(357,369)(358,370)(359,372)(360,371)
(361,377)(362,378)(363,380)(364,379)(365,381)(366,382)(367,384)(368,383);;
s2 := ( 1,225)( 2,227)( 3,226)( 4,228)( 5,233)( 6,235)( 7,234)( 8,236)
( 9,229)( 10,231)( 11,230)( 12,232)( 13,237)( 14,239)( 15,238)( 16,240)
( 17,209)( 18,211)( 19,210)( 20,212)( 21,217)( 22,219)( 23,218)( 24,220)
( 25,213)( 26,215)( 27,214)( 28,216)( 29,221)( 30,223)( 31,222)( 32,224)
( 33,193)( 34,195)( 35,194)( 36,196)( 37,201)( 38,203)( 39,202)( 40,204)
( 41,197)( 42,199)( 43,198)( 44,200)( 45,205)( 46,207)( 47,206)( 48,208)
( 49,273)( 50,275)( 51,274)( 52,276)( 53,281)( 54,283)( 55,282)( 56,284)
( 57,277)( 58,279)( 59,278)( 60,280)( 61,285)( 62,287)( 63,286)( 64,288)
( 65,257)( 66,259)( 67,258)( 68,260)( 69,265)( 70,267)( 71,266)( 72,268)
( 73,261)( 74,263)( 75,262)( 76,264)( 77,269)( 78,271)( 79,270)( 80,272)
( 81,241)( 82,243)( 83,242)( 84,244)( 85,249)( 86,251)( 87,250)( 88,252)
( 89,245)( 90,247)( 91,246)( 92,248)( 93,253)( 94,255)( 95,254)( 96,256)
( 97,321)( 98,323)( 99,322)(100,324)(101,329)(102,331)(103,330)(104,332)
(105,325)(106,327)(107,326)(108,328)(109,333)(110,335)(111,334)(112,336)
(113,305)(114,307)(115,306)(116,308)(117,313)(118,315)(119,314)(120,316)
(121,309)(122,311)(123,310)(124,312)(125,317)(126,319)(127,318)(128,320)
(129,289)(130,291)(131,290)(132,292)(133,297)(134,299)(135,298)(136,300)
(137,293)(138,295)(139,294)(140,296)(141,301)(142,303)(143,302)(144,304)
(145,369)(146,371)(147,370)(148,372)(149,377)(150,379)(151,378)(152,380)
(153,373)(154,375)(155,374)(156,376)(157,381)(158,383)(159,382)(160,384)
(161,353)(162,355)(163,354)(164,356)(165,361)(166,363)(167,362)(168,364)
(169,357)(170,359)(171,358)(172,360)(173,365)(174,367)(175,366)(176,368)
(177,337)(178,339)(179,338)(180,340)(181,345)(182,347)(183,346)(184,348)
(185,341)(186,343)(187,342)(188,344)(189,349)(190,351)(191,350)(192,352);;
s3 := ( 1, 97)( 2, 98)( 3,100)( 4, 99)( 5,101)( 6,102)( 7,104)( 8,103)
( 9,109)( 10,110)( 11,112)( 12,111)( 13,105)( 14,106)( 15,108)( 16,107)
( 17,129)( 18,130)( 19,132)( 20,131)( 21,133)( 22,134)( 23,136)( 24,135)
( 25,141)( 26,142)( 27,144)( 28,143)( 29,137)( 30,138)( 31,140)( 32,139)
( 33,113)( 34,114)( 35,116)( 36,115)( 37,117)( 38,118)( 39,120)( 40,119)
( 41,125)( 42,126)( 43,128)( 44,127)( 45,121)( 46,122)( 47,124)( 48,123)
( 49,145)( 50,146)( 51,148)( 52,147)( 53,149)( 54,150)( 55,152)( 56,151)
( 57,157)( 58,158)( 59,160)( 60,159)( 61,153)( 62,154)( 63,156)( 64,155)
( 65,177)( 66,178)( 67,180)( 68,179)( 69,181)( 70,182)( 71,184)( 72,183)
( 73,189)( 74,190)( 75,192)( 76,191)( 77,185)( 78,186)( 79,188)( 80,187)
( 81,161)( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)
( 89,173)( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)
(193,289)(194,290)(195,292)(196,291)(197,293)(198,294)(199,296)(200,295)
(201,301)(202,302)(203,304)(204,303)(205,297)(206,298)(207,300)(208,299)
(209,321)(210,322)(211,324)(212,323)(213,325)(214,326)(215,328)(216,327)
(217,333)(218,334)(219,336)(220,335)(221,329)(222,330)(223,332)(224,331)
(225,305)(226,306)(227,308)(228,307)(229,309)(230,310)(231,312)(232,311)
(233,317)(234,318)(235,320)(236,319)(237,313)(238,314)(239,316)(240,315)
(241,337)(242,338)(243,340)(244,339)(245,341)(246,342)(247,344)(248,343)
(249,349)(250,350)(251,352)(252,351)(253,345)(254,346)(255,348)(256,347)
(257,369)(258,370)(259,372)(260,371)(261,373)(262,374)(263,376)(264,375)
(265,381)(266,382)(267,384)(268,383)(269,377)(270,378)(271,380)(272,379)
(273,353)(274,354)(275,356)(276,355)(277,357)(278,358)(279,360)(280,359)
(281,365)(282,366)(283,368)(284,367)(285,361)(286,362)(287,364)(288,363);;
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*s0*s1*s2*s3*s1*s2*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1, 49)( 2, 50)( 3, 51)( 4, 52)( 5, 54)( 6, 53)( 7, 56)
( 8, 55)( 9, 59)( 10, 60)( 11, 57)( 12, 58)( 13, 64)( 14, 63)( 15, 62)
( 16, 61)( 17, 65)( 18, 66)( 19, 67)( 20, 68)( 21, 70)( 22, 69)( 23, 72)
( 24, 71)( 25, 75)( 26, 76)( 27, 73)( 28, 74)( 29, 80)( 30, 79)( 31, 78)
( 32, 77)( 33, 81)( 34, 82)( 35, 83)( 36, 84)( 37, 86)( 38, 85)( 39, 88)
( 40, 87)( 41, 91)( 42, 92)( 43, 89)( 44, 90)( 45, 96)( 46, 95)( 47, 94)
( 48, 93)( 97,145)( 98,146)( 99,147)(100,148)(101,150)(102,149)(103,152)
(104,151)(105,155)(106,156)(107,153)(108,154)(109,160)(110,159)(111,158)
(112,157)(113,161)(114,162)(115,163)(116,164)(117,166)(118,165)(119,168)
(120,167)(121,171)(122,172)(123,169)(124,170)(125,176)(126,175)(127,174)
(128,173)(129,177)(130,178)(131,179)(132,180)(133,182)(134,181)(135,184)
(136,183)(137,187)(138,188)(139,185)(140,186)(141,192)(142,191)(143,190)
(144,189)(193,241)(194,242)(195,243)(196,244)(197,246)(198,245)(199,248)
(200,247)(201,251)(202,252)(203,249)(204,250)(205,256)(206,255)(207,254)
(208,253)(209,257)(210,258)(211,259)(212,260)(213,262)(214,261)(215,264)
(216,263)(217,267)(218,268)(219,265)(220,266)(221,272)(222,271)(223,270)
(224,269)(225,273)(226,274)(227,275)(228,276)(229,278)(230,277)(231,280)
(232,279)(233,283)(234,284)(235,281)(236,282)(237,288)(238,287)(239,286)
(240,285)(289,337)(290,338)(291,339)(292,340)(293,342)(294,341)(295,344)
(296,343)(297,347)(298,348)(299,345)(300,346)(301,352)(302,351)(303,350)
(304,349)(305,353)(306,354)(307,355)(308,356)(309,358)(310,357)(311,360)
(312,359)(313,363)(314,364)(315,361)(316,362)(317,368)(318,367)(319,366)
(320,365)(321,369)(322,370)(323,371)(324,372)(325,374)(326,373)(327,376)
(328,375)(329,379)(330,380)(331,377)(332,378)(333,384)(334,383)(335,382)
(336,381);
s1 := Sym(384)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 15, 16)( 17, 37)
( 18, 38)( 19, 40)( 20, 39)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 25, 41)
( 26, 42)( 27, 44)( 28, 43)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 49, 53)
( 50, 54)( 51, 56)( 52, 55)( 59, 60)( 63, 64)( 65, 85)( 66, 86)( 67, 88)
( 68, 87)( 69, 81)( 70, 82)( 71, 84)( 72, 83)( 73, 89)( 74, 90)( 75, 92)
( 76, 91)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 97,101)( 98,102)( 99,104)
(100,103)(107,108)(111,112)(113,133)(114,134)(115,136)(116,135)(117,129)
(118,130)(119,132)(120,131)(121,137)(122,138)(123,140)(124,139)(125,141)
(126,142)(127,144)(128,143)(145,149)(146,150)(147,152)(148,151)(155,156)
(159,160)(161,181)(162,182)(163,184)(164,183)(165,177)(166,178)(167,180)
(168,179)(169,185)(170,186)(171,188)(172,187)(173,189)(174,190)(175,192)
(176,191)(193,197)(194,198)(195,200)(196,199)(203,204)(207,208)(209,229)
(210,230)(211,232)(212,231)(213,225)(214,226)(215,228)(216,227)(217,233)
(218,234)(219,236)(220,235)(221,237)(222,238)(223,240)(224,239)(241,245)
(242,246)(243,248)(244,247)(251,252)(255,256)(257,277)(258,278)(259,280)
(260,279)(261,273)(262,274)(263,276)(264,275)(265,281)(266,282)(267,284)
(268,283)(269,285)(270,286)(271,288)(272,287)(289,293)(290,294)(291,296)
(292,295)(299,300)(303,304)(305,325)(306,326)(307,328)(308,327)(309,321)
(310,322)(311,324)(312,323)(313,329)(314,330)(315,332)(316,331)(317,333)
(318,334)(319,336)(320,335)(337,341)(338,342)(339,344)(340,343)(347,348)
(351,352)(353,373)(354,374)(355,376)(356,375)(357,369)(358,370)(359,372)
(360,371)(361,377)(362,378)(363,380)(364,379)(365,381)(366,382)(367,384)
(368,383);
s2 := Sym(384)!( 1,225)( 2,227)( 3,226)( 4,228)( 5,233)( 6,235)( 7,234)
( 8,236)( 9,229)( 10,231)( 11,230)( 12,232)( 13,237)( 14,239)( 15,238)
( 16,240)( 17,209)( 18,211)( 19,210)( 20,212)( 21,217)( 22,219)( 23,218)
( 24,220)( 25,213)( 26,215)( 27,214)( 28,216)( 29,221)( 30,223)( 31,222)
( 32,224)( 33,193)( 34,195)( 35,194)( 36,196)( 37,201)( 38,203)( 39,202)
( 40,204)( 41,197)( 42,199)( 43,198)( 44,200)( 45,205)( 46,207)( 47,206)
( 48,208)( 49,273)( 50,275)( 51,274)( 52,276)( 53,281)( 54,283)( 55,282)
( 56,284)( 57,277)( 58,279)( 59,278)( 60,280)( 61,285)( 62,287)( 63,286)
( 64,288)( 65,257)( 66,259)( 67,258)( 68,260)( 69,265)( 70,267)( 71,266)
( 72,268)( 73,261)( 74,263)( 75,262)( 76,264)( 77,269)( 78,271)( 79,270)
( 80,272)( 81,241)( 82,243)( 83,242)( 84,244)( 85,249)( 86,251)( 87,250)
( 88,252)( 89,245)( 90,247)( 91,246)( 92,248)( 93,253)( 94,255)( 95,254)
( 96,256)( 97,321)( 98,323)( 99,322)(100,324)(101,329)(102,331)(103,330)
(104,332)(105,325)(106,327)(107,326)(108,328)(109,333)(110,335)(111,334)
(112,336)(113,305)(114,307)(115,306)(116,308)(117,313)(118,315)(119,314)
(120,316)(121,309)(122,311)(123,310)(124,312)(125,317)(126,319)(127,318)
(128,320)(129,289)(130,291)(131,290)(132,292)(133,297)(134,299)(135,298)
(136,300)(137,293)(138,295)(139,294)(140,296)(141,301)(142,303)(143,302)
(144,304)(145,369)(146,371)(147,370)(148,372)(149,377)(150,379)(151,378)
(152,380)(153,373)(154,375)(155,374)(156,376)(157,381)(158,383)(159,382)
(160,384)(161,353)(162,355)(163,354)(164,356)(165,361)(166,363)(167,362)
(168,364)(169,357)(170,359)(171,358)(172,360)(173,365)(174,367)(175,366)
(176,368)(177,337)(178,339)(179,338)(180,340)(181,345)(182,347)(183,346)
(184,348)(185,341)(186,343)(187,342)(188,344)(189,349)(190,351)(191,350)
(192,352);
s3 := Sym(384)!( 1, 97)( 2, 98)( 3,100)( 4, 99)( 5,101)( 6,102)( 7,104)
( 8,103)( 9,109)( 10,110)( 11,112)( 12,111)( 13,105)( 14,106)( 15,108)
( 16,107)( 17,129)( 18,130)( 19,132)( 20,131)( 21,133)( 22,134)( 23,136)
( 24,135)( 25,141)( 26,142)( 27,144)( 28,143)( 29,137)( 30,138)( 31,140)
( 32,139)( 33,113)( 34,114)( 35,116)( 36,115)( 37,117)( 38,118)( 39,120)
( 40,119)( 41,125)( 42,126)( 43,128)( 44,127)( 45,121)( 46,122)( 47,124)
( 48,123)( 49,145)( 50,146)( 51,148)( 52,147)( 53,149)( 54,150)( 55,152)
( 56,151)( 57,157)( 58,158)( 59,160)( 60,159)( 61,153)( 62,154)( 63,156)
( 64,155)( 65,177)( 66,178)( 67,180)( 68,179)( 69,181)( 70,182)( 71,184)
( 72,183)( 73,189)( 74,190)( 75,192)( 76,191)( 77,185)( 78,186)( 79,188)
( 80,187)( 81,161)( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)
( 88,167)( 89,173)( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)
( 96,171)(193,289)(194,290)(195,292)(196,291)(197,293)(198,294)(199,296)
(200,295)(201,301)(202,302)(203,304)(204,303)(205,297)(206,298)(207,300)
(208,299)(209,321)(210,322)(211,324)(212,323)(213,325)(214,326)(215,328)
(216,327)(217,333)(218,334)(219,336)(220,335)(221,329)(222,330)(223,332)
(224,331)(225,305)(226,306)(227,308)(228,307)(229,309)(230,310)(231,312)
(232,311)(233,317)(234,318)(235,320)(236,319)(237,313)(238,314)(239,316)
(240,315)(241,337)(242,338)(243,340)(244,339)(245,341)(246,342)(247,344)
(248,343)(249,349)(250,350)(251,352)(252,351)(253,345)(254,346)(255,348)
(256,347)(257,369)(258,370)(259,372)(260,371)(261,373)(262,374)(263,376)
(264,375)(265,381)(266,382)(267,384)(268,383)(269,377)(270,378)(271,380)
(272,379)(273,353)(274,354)(275,356)(276,355)(277,357)(278,358)(279,360)
(280,359)(281,365)(282,366)(283,368)(284,367)(285,361)(286,362)(287,364)
(288,363);
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*s0*s1*s2*s3*s1*s2*s1*s0*s1*s2*s0*s1 >;
References : None.
to this polytope