Polytope of Type {4,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,4}*768l
if this polytope has a name.
Group : SmallGroup(768,1090234)
Rank : 4
Schlafli Type : {4,6,4}
Number of vertices, edges, etc : 8, 48, 48, 8
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Orientable
Flat
Self-Dual
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 : {4,3,4}*384, {4,6,4}*384c, {4,6,4}*384d, {4,6,4}*384e, {4,6,4}*384f
4-fold quotients : {2,6,4}*192, {4,6,2}*192, {4,3,4}*192a, {4,3,4}*192b, {4,6,4}*192d, {4,6,4}*192e, {4,6,4}*192f, {4,6,4}*192g
8-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c, {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c, {4,3,4}*96
16-fold quotients : {2,3,4}*48, {4,3,2}*48, {2,6,2}*48
32-fold quotients : {2,3,2}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,196)( 2,195)( 3,194)( 4,193)( 5,200)( 6,199)( 7,198)( 8,197)
( 9,204)( 10,203)( 11,202)( 12,201)( 13,208)( 14,207)( 15,206)( 16,205)
( 17,212)( 18,211)( 19,210)( 20,209)( 21,216)( 22,215)( 23,214)( 24,213)
( 25,220)( 26,219)( 27,218)( 28,217)( 29,224)( 30,223)( 31,222)( 32,221)
( 33,228)( 34,227)( 35,226)( 36,225)( 37,232)( 38,231)( 39,230)( 40,229)
( 41,236)( 42,235)( 43,234)( 44,233)( 45,240)( 46,239)( 47,238)( 48,237)
( 49,244)( 50,243)( 51,242)( 52,241)( 53,248)( 54,247)( 55,246)( 56,245)
( 57,252)( 58,251)( 59,250)( 60,249)( 61,256)( 62,255)( 63,254)( 64,253)
( 65,260)( 66,259)( 67,258)( 68,257)( 69,264)( 70,263)( 71,262)( 72,261)
( 73,268)( 74,267)( 75,266)( 76,265)( 77,272)( 78,271)( 79,270)( 80,269)
( 81,276)( 82,275)( 83,274)( 84,273)( 85,280)( 86,279)( 87,278)( 88,277)
( 89,284)( 90,283)( 91,282)( 92,281)( 93,288)( 94,287)( 95,286)( 96,285)
( 97,292)( 98,291)( 99,290)(100,289)(101,296)(102,295)(103,294)(104,293)
(105,300)(106,299)(107,298)(108,297)(109,304)(110,303)(111,302)(112,301)
(113,308)(114,307)(115,306)(116,305)(117,312)(118,311)(119,310)(120,309)
(121,316)(122,315)(123,314)(124,313)(125,320)(126,319)(127,318)(128,317)
(129,324)(130,323)(131,322)(132,321)(133,328)(134,327)(135,326)(136,325)
(137,332)(138,331)(139,330)(140,329)(141,336)(142,335)(143,334)(144,333)
(145,340)(146,339)(147,338)(148,337)(149,344)(150,343)(151,342)(152,341)
(153,348)(154,347)(155,346)(156,345)(157,352)(158,351)(159,350)(160,349)
(161,356)(162,355)(163,354)(164,353)(165,360)(166,359)(167,358)(168,357)
(169,364)(170,363)(171,362)(172,361)(173,368)(174,367)(175,366)(176,365)
(177,372)(178,371)(179,370)(180,369)(181,376)(182,375)(183,374)(184,373)
(185,380)(186,379)(187,378)(188,377)(189,384)(190,383)(191,382)(192,381);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)( 55, 56)
( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)( 68, 83)
( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 93)( 74, 94)( 75, 96)( 76, 95)
( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 99,100)(103,104)(105,109)(106,110)
(107,112)(108,111)(113,129)(114,130)(115,132)(116,131)(117,133)(118,134)
(119,136)(120,135)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)
(127,140)(128,139)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)
(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)
(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)
(195,196)(199,200)(201,205)(202,206)(203,208)(204,207)(209,225)(210,226)
(211,228)(212,227)(213,229)(214,230)(215,232)(216,231)(217,237)(218,238)
(219,240)(220,239)(221,233)(222,234)(223,236)(224,235)(243,244)(247,248)
(249,253)(250,254)(251,256)(252,255)(257,273)(258,274)(259,276)(260,275)
(261,277)(262,278)(263,280)(264,279)(265,285)(266,286)(267,288)(268,287)
(269,281)(270,282)(271,284)(272,283)(291,292)(295,296)(297,301)(298,302)
(299,304)(300,303)(305,321)(306,322)(307,324)(308,323)(309,325)(310,326)
(311,328)(312,327)(313,333)(314,334)(315,336)(316,335)(317,329)(318,330)
(319,332)(320,331)(339,340)(343,344)(345,349)(346,350)(347,352)(348,351)
(353,369)(354,370)(355,372)(356,371)(357,373)(358,374)(359,376)(360,375)
(361,381)(362,382)(363,384)(364,383)(365,377)(366,378)(367,380)(368,379);;
s2 := ( 1,129)( 2,131)( 3,130)( 4,132)( 5,137)( 6,139)( 7,138)( 8,140)
( 9,133)( 10,135)( 11,134)( 12,136)( 13,141)( 14,143)( 15,142)( 16,144)
( 17,113)( 18,115)( 19,114)( 20,116)( 21,121)( 22,123)( 23,122)( 24,124)
( 25,117)( 26,119)( 27,118)( 28,120)( 29,125)( 30,127)( 31,126)( 32,128)
( 33, 97)( 34, 99)( 35, 98)( 36,100)( 37,105)( 38,107)( 39,106)( 40,108)
( 41,101)( 42,103)( 43,102)( 44,104)( 45,109)( 46,111)( 47,110)( 48,112)
( 49,177)( 50,179)( 51,178)( 52,180)( 53,185)( 54,187)( 55,186)( 56,188)
( 57,181)( 58,183)( 59,182)( 60,184)( 61,189)( 62,191)( 63,190)( 64,192)
( 65,161)( 66,163)( 67,162)( 68,164)( 69,169)( 70,171)( 71,170)( 72,172)
( 73,165)( 74,167)( 75,166)( 76,168)( 77,173)( 78,175)( 79,174)( 80,176)
( 81,145)( 82,147)( 83,146)( 84,148)( 85,153)( 86,155)( 87,154)( 88,156)
( 89,149)( 90,151)( 91,150)( 92,152)( 93,157)( 94,159)( 95,158)( 96,160)
(193,321)(194,323)(195,322)(196,324)(197,329)(198,331)(199,330)(200,332)
(201,325)(202,327)(203,326)(204,328)(205,333)(206,335)(207,334)(208,336)
(209,305)(210,307)(211,306)(212,308)(213,313)(214,315)(215,314)(216,316)
(217,309)(218,311)(219,310)(220,312)(221,317)(222,319)(223,318)(224,320)
(225,289)(226,291)(227,290)(228,292)(229,297)(230,299)(231,298)(232,300)
(233,293)(234,295)(235,294)(236,296)(237,301)(238,303)(239,302)(240,304)
(241,369)(242,371)(243,370)(244,372)(245,377)(246,379)(247,378)(248,380)
(249,373)(250,375)(251,374)(252,376)(253,381)(254,383)(255,382)(256,384)
(257,353)(258,355)(259,354)(260,356)(261,361)(262,363)(263,362)(264,364)
(265,357)(266,359)(267,358)(268,360)(269,365)(270,367)(271,366)(272,368)
(273,337)(274,339)(275,338)(276,340)(277,345)(278,347)(279,346)(280,348)
(281,341)(282,343)(283,342)(284,344)(285,349)(286,351)(287,350)(288,352);;
s3 := ( 1, 53)( 2, 54)( 3, 55)( 4, 56)( 5, 49)( 6, 50)( 7, 51)( 8, 52)
( 9, 61)( 10, 62)( 11, 63)( 12, 64)( 13, 57)( 14, 58)( 15, 59)( 16, 60)
( 17, 69)( 18, 70)( 19, 71)( 20, 72)( 21, 65)( 22, 66)( 23, 67)( 24, 68)
( 25, 77)( 26, 78)( 27, 79)( 28, 80)( 29, 73)( 30, 74)( 31, 75)( 32, 76)
( 33, 85)( 34, 86)( 35, 87)( 36, 88)( 37, 81)( 38, 82)( 39, 83)( 40, 84)
( 41, 93)( 42, 94)( 43, 95)( 44, 96)( 45, 89)( 46, 90)( 47, 91)( 48, 92)
( 97,149)( 98,150)( 99,151)(100,152)(101,145)(102,146)(103,147)(104,148)
(105,157)(106,158)(107,159)(108,160)(109,153)(110,154)(111,155)(112,156)
(113,165)(114,166)(115,167)(116,168)(117,161)(118,162)(119,163)(120,164)
(121,173)(122,174)(123,175)(124,176)(125,169)(126,170)(127,171)(128,172)
(129,181)(130,182)(131,183)(132,184)(133,177)(134,178)(135,179)(136,180)
(137,189)(138,190)(139,191)(140,192)(141,185)(142,186)(143,187)(144,188)
(193,245)(194,246)(195,247)(196,248)(197,241)(198,242)(199,243)(200,244)
(201,253)(202,254)(203,255)(204,256)(205,249)(206,250)(207,251)(208,252)
(209,261)(210,262)(211,263)(212,264)(213,257)(214,258)(215,259)(216,260)
(217,269)(218,270)(219,271)(220,272)(221,265)(222,266)(223,267)(224,268)
(225,277)(226,278)(227,279)(228,280)(229,273)(230,274)(231,275)(232,276)
(233,285)(234,286)(235,287)(236,288)(237,281)(238,282)(239,283)(240,284)
(289,341)(290,342)(291,343)(292,344)(293,337)(294,338)(295,339)(296,340)
(297,349)(298,350)(299,351)(300,352)(301,345)(302,346)(303,347)(304,348)
(305,357)(306,358)(307,359)(308,360)(309,353)(310,354)(311,355)(312,356)
(313,365)(314,366)(315,367)(316,368)(317,361)(318,362)(319,363)(320,364)
(321,373)(322,374)(323,375)(324,376)(325,369)(326,370)(327,371)(328,372)
(329,381)(330,382)(331,383)(332,384)(333,377)(334,378)(335,379)(336,380);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1,196)( 2,195)( 3,194)( 4,193)( 5,200)( 6,199)( 7,198)
( 8,197)( 9,204)( 10,203)( 11,202)( 12,201)( 13,208)( 14,207)( 15,206)
( 16,205)( 17,212)( 18,211)( 19,210)( 20,209)( 21,216)( 22,215)( 23,214)
( 24,213)( 25,220)( 26,219)( 27,218)( 28,217)( 29,224)( 30,223)( 31,222)
( 32,221)( 33,228)( 34,227)( 35,226)( 36,225)( 37,232)( 38,231)( 39,230)
( 40,229)( 41,236)( 42,235)( 43,234)( 44,233)( 45,240)( 46,239)( 47,238)
( 48,237)( 49,244)( 50,243)( 51,242)( 52,241)( 53,248)( 54,247)( 55,246)
( 56,245)( 57,252)( 58,251)( 59,250)( 60,249)( 61,256)( 62,255)( 63,254)
( 64,253)( 65,260)( 66,259)( 67,258)( 68,257)( 69,264)( 70,263)( 71,262)
( 72,261)( 73,268)( 74,267)( 75,266)( 76,265)( 77,272)( 78,271)( 79,270)
( 80,269)( 81,276)( 82,275)( 83,274)( 84,273)( 85,280)( 86,279)( 87,278)
( 88,277)( 89,284)( 90,283)( 91,282)( 92,281)( 93,288)( 94,287)( 95,286)
( 96,285)( 97,292)( 98,291)( 99,290)(100,289)(101,296)(102,295)(103,294)
(104,293)(105,300)(106,299)(107,298)(108,297)(109,304)(110,303)(111,302)
(112,301)(113,308)(114,307)(115,306)(116,305)(117,312)(118,311)(119,310)
(120,309)(121,316)(122,315)(123,314)(124,313)(125,320)(126,319)(127,318)
(128,317)(129,324)(130,323)(131,322)(132,321)(133,328)(134,327)(135,326)
(136,325)(137,332)(138,331)(139,330)(140,329)(141,336)(142,335)(143,334)
(144,333)(145,340)(146,339)(147,338)(148,337)(149,344)(150,343)(151,342)
(152,341)(153,348)(154,347)(155,346)(156,345)(157,352)(158,351)(159,350)
(160,349)(161,356)(162,355)(163,354)(164,353)(165,360)(166,359)(167,358)
(168,357)(169,364)(170,363)(171,362)(172,361)(173,368)(174,367)(175,366)
(176,365)(177,372)(178,371)(179,370)(180,369)(181,376)(182,375)(183,374)
(184,373)(185,380)(186,379)(187,378)(188,377)(189,384)(190,383)(191,382)
(192,381);
s1 := Sym(384)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)
( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)
( 55, 56)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)
( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 93)( 74, 94)( 75, 96)
( 76, 95)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 99,100)(103,104)(105,109)
(106,110)(107,112)(108,111)(113,129)(114,130)(115,132)(116,131)(117,133)
(118,134)(119,136)(120,135)(121,141)(122,142)(123,144)(124,143)(125,137)
(126,138)(127,140)(128,139)(147,148)(151,152)(153,157)(154,158)(155,160)
(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)
(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)
(176,187)(195,196)(199,200)(201,205)(202,206)(203,208)(204,207)(209,225)
(210,226)(211,228)(212,227)(213,229)(214,230)(215,232)(216,231)(217,237)
(218,238)(219,240)(220,239)(221,233)(222,234)(223,236)(224,235)(243,244)
(247,248)(249,253)(250,254)(251,256)(252,255)(257,273)(258,274)(259,276)
(260,275)(261,277)(262,278)(263,280)(264,279)(265,285)(266,286)(267,288)
(268,287)(269,281)(270,282)(271,284)(272,283)(291,292)(295,296)(297,301)
(298,302)(299,304)(300,303)(305,321)(306,322)(307,324)(308,323)(309,325)
(310,326)(311,328)(312,327)(313,333)(314,334)(315,336)(316,335)(317,329)
(318,330)(319,332)(320,331)(339,340)(343,344)(345,349)(346,350)(347,352)
(348,351)(353,369)(354,370)(355,372)(356,371)(357,373)(358,374)(359,376)
(360,375)(361,381)(362,382)(363,384)(364,383)(365,377)(366,378)(367,380)
(368,379);
s2 := Sym(384)!( 1,129)( 2,131)( 3,130)( 4,132)( 5,137)( 6,139)( 7,138)
( 8,140)( 9,133)( 10,135)( 11,134)( 12,136)( 13,141)( 14,143)( 15,142)
( 16,144)( 17,113)( 18,115)( 19,114)( 20,116)( 21,121)( 22,123)( 23,122)
( 24,124)( 25,117)( 26,119)( 27,118)( 28,120)( 29,125)( 30,127)( 31,126)
( 32,128)( 33, 97)( 34, 99)( 35, 98)( 36,100)( 37,105)( 38,107)( 39,106)
( 40,108)( 41,101)( 42,103)( 43,102)( 44,104)( 45,109)( 46,111)( 47,110)
( 48,112)( 49,177)( 50,179)( 51,178)( 52,180)( 53,185)( 54,187)( 55,186)
( 56,188)( 57,181)( 58,183)( 59,182)( 60,184)( 61,189)( 62,191)( 63,190)
( 64,192)( 65,161)( 66,163)( 67,162)( 68,164)( 69,169)( 70,171)( 71,170)
( 72,172)( 73,165)( 74,167)( 75,166)( 76,168)( 77,173)( 78,175)( 79,174)
( 80,176)( 81,145)( 82,147)( 83,146)( 84,148)( 85,153)( 86,155)( 87,154)
( 88,156)( 89,149)( 90,151)( 91,150)( 92,152)( 93,157)( 94,159)( 95,158)
( 96,160)(193,321)(194,323)(195,322)(196,324)(197,329)(198,331)(199,330)
(200,332)(201,325)(202,327)(203,326)(204,328)(205,333)(206,335)(207,334)
(208,336)(209,305)(210,307)(211,306)(212,308)(213,313)(214,315)(215,314)
(216,316)(217,309)(218,311)(219,310)(220,312)(221,317)(222,319)(223,318)
(224,320)(225,289)(226,291)(227,290)(228,292)(229,297)(230,299)(231,298)
(232,300)(233,293)(234,295)(235,294)(236,296)(237,301)(238,303)(239,302)
(240,304)(241,369)(242,371)(243,370)(244,372)(245,377)(246,379)(247,378)
(248,380)(249,373)(250,375)(251,374)(252,376)(253,381)(254,383)(255,382)
(256,384)(257,353)(258,355)(259,354)(260,356)(261,361)(262,363)(263,362)
(264,364)(265,357)(266,359)(267,358)(268,360)(269,365)(270,367)(271,366)
(272,368)(273,337)(274,339)(275,338)(276,340)(277,345)(278,347)(279,346)
(280,348)(281,341)(282,343)(283,342)(284,344)(285,349)(286,351)(287,350)
(288,352);
s3 := Sym(384)!( 1, 53)( 2, 54)( 3, 55)( 4, 56)( 5, 49)( 6, 50)( 7, 51)
( 8, 52)( 9, 61)( 10, 62)( 11, 63)( 12, 64)( 13, 57)( 14, 58)( 15, 59)
( 16, 60)( 17, 69)( 18, 70)( 19, 71)( 20, 72)( 21, 65)( 22, 66)( 23, 67)
( 24, 68)( 25, 77)( 26, 78)( 27, 79)( 28, 80)( 29, 73)( 30, 74)( 31, 75)
( 32, 76)( 33, 85)( 34, 86)( 35, 87)( 36, 88)( 37, 81)( 38, 82)( 39, 83)
( 40, 84)( 41, 93)( 42, 94)( 43, 95)( 44, 96)( 45, 89)( 46, 90)( 47, 91)
( 48, 92)( 97,149)( 98,150)( 99,151)(100,152)(101,145)(102,146)(103,147)
(104,148)(105,157)(106,158)(107,159)(108,160)(109,153)(110,154)(111,155)
(112,156)(113,165)(114,166)(115,167)(116,168)(117,161)(118,162)(119,163)
(120,164)(121,173)(122,174)(123,175)(124,176)(125,169)(126,170)(127,171)
(128,172)(129,181)(130,182)(131,183)(132,184)(133,177)(134,178)(135,179)
(136,180)(137,189)(138,190)(139,191)(140,192)(141,185)(142,186)(143,187)
(144,188)(193,245)(194,246)(195,247)(196,248)(197,241)(198,242)(199,243)
(200,244)(201,253)(202,254)(203,255)(204,256)(205,249)(206,250)(207,251)
(208,252)(209,261)(210,262)(211,263)(212,264)(213,257)(214,258)(215,259)
(216,260)(217,269)(218,270)(219,271)(220,272)(221,265)(222,266)(223,267)
(224,268)(225,277)(226,278)(227,279)(228,280)(229,273)(230,274)(231,275)
(232,276)(233,285)(234,286)(235,287)(236,288)(237,281)(238,282)(239,283)
(240,284)(289,341)(290,342)(291,343)(292,344)(293,337)(294,338)(295,339)
(296,340)(297,349)(298,350)(299,351)(300,352)(301,345)(302,346)(303,347)
(304,348)(305,357)(306,358)(307,359)(308,360)(309,353)(310,354)(311,355)
(312,356)(313,365)(314,366)(315,367)(316,368)(317,361)(318,362)(319,363)
(320,364)(321,373)(322,374)(323,375)(324,376)(325,369)(326,370)(327,371)
(328,372)(329,381)(330,382)(331,383)(332,384)(333,377)(334,378)(335,379)
(336,380);
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, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*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 >;
References : None.
to this polytope