Polytope of Type {6,16,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,16,4}*768a
Also Known As : {{6,16|2},{16,4|2}}. if this polytope has another name.
Group : SmallGroup(768,323301)
Rank : 4
Schlafli Type : {6,16,4}
Number of vertices, edges, etc : 6, 48, 32, 4
Order of s0s1s2s3 : 48
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {6,8,4}*384a, {6,16,2}*384
3-fold quotients : {2,16,4}*256a
4-fold quotients : {6,4,4}*192, {6,8,2}*192
6-fold quotients : {2,8,4}*128a, {2,16,2}*128
8-fold quotients : {6,2,4}*96, {6,4,2}*96a
12-fold quotients : {2,4,4}*64, {2,8,2}*64
16-fold quotients : {3,2,4}*48, {6,2,2}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32
32-fold quotients : {3,2,2}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 49)( 2, 51)( 3, 50)( 4, 52)( 5, 54)( 6, 53)( 7, 55)( 8, 57)
( 9, 56)( 10, 58)( 11, 60)( 12, 59)( 13, 61)( 14, 63)( 15, 62)( 16, 64)
( 17, 66)( 18, 65)( 19, 67)( 20, 69)( 21, 68)( 22, 70)( 23, 72)( 24, 71)
( 25, 73)( 26, 75)( 27, 74)( 28, 76)( 29, 78)( 30, 77)( 31, 79)( 32, 81)
( 33, 80)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 87)( 39, 86)( 40, 88)
( 41, 90)( 42, 89)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 96)( 48, 95)
( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,151)(104,153)
(105,152)(106,154)(107,156)(108,155)(109,157)(110,159)(111,158)(112,160)
(113,162)(114,161)(115,163)(116,165)(117,164)(118,166)(119,168)(120,167)
(121,169)(122,171)(123,170)(124,172)(125,174)(126,173)(127,175)(128,177)
(129,176)(130,178)(131,180)(132,179)(133,181)(134,183)(135,182)(136,184)
(137,186)(138,185)(139,187)(140,189)(141,188)(142,190)(143,192)(144,191)
(193,241)(194,243)(195,242)(196,244)(197,246)(198,245)(199,247)(200,249)
(201,248)(202,250)(203,252)(204,251)(205,253)(206,255)(207,254)(208,256)
(209,258)(210,257)(211,259)(212,261)(213,260)(214,262)(215,264)(216,263)
(217,265)(218,267)(219,266)(220,268)(221,270)(222,269)(223,271)(224,273)
(225,272)(226,274)(227,276)(228,275)(229,277)(230,279)(231,278)(232,280)
(233,282)(234,281)(235,283)(236,285)(237,284)(238,286)(239,288)(240,287)
(289,337)(290,339)(291,338)(292,340)(293,342)(294,341)(295,343)(296,345)
(297,344)(298,346)(299,348)(300,347)(301,349)(302,351)(303,350)(304,352)
(305,354)(306,353)(307,355)(308,357)(309,356)(310,358)(311,360)(312,359)
(313,361)(314,363)(315,362)(316,364)(317,366)(318,365)(319,367)(320,369)
(321,368)(322,370)(323,372)(324,371)(325,373)(326,375)(327,374)(328,376)
(329,378)(330,377)(331,379)(332,381)(333,380)(334,382)(335,384)(336,383);;
s1 := ( 1,243)( 2,242)( 3,241)( 4,246)( 5,245)( 6,244)( 7,252)( 8,251)
( 9,250)( 10,249)( 11,248)( 12,247)( 13,255)( 14,254)( 15,253)( 16,258)
( 17,257)( 18,256)( 19,264)( 20,263)( 21,262)( 22,261)( 23,260)( 24,259)
( 25,273)( 26,272)( 27,271)( 28,276)( 29,275)( 30,274)( 31,267)( 32,266)
( 33,265)( 34,270)( 35,269)( 36,268)( 37,285)( 38,284)( 39,283)( 40,288)
( 41,287)( 42,286)( 43,279)( 44,278)( 45,277)( 46,282)( 47,281)( 48,280)
( 49,195)( 50,194)( 51,193)( 52,198)( 53,197)( 54,196)( 55,204)( 56,203)
( 57,202)( 58,201)( 59,200)( 60,199)( 61,207)( 62,206)( 63,205)( 64,210)
( 65,209)( 66,208)( 67,216)( 68,215)( 69,214)( 70,213)( 71,212)( 72,211)
( 73,225)( 74,224)( 75,223)( 76,228)( 77,227)( 78,226)( 79,219)( 80,218)
( 81,217)( 82,222)( 83,221)( 84,220)( 85,237)( 86,236)( 87,235)( 88,240)
( 89,239)( 90,238)( 91,231)( 92,230)( 93,229)( 94,234)( 95,233)( 96,232)
( 97,339)( 98,338)( 99,337)(100,342)(101,341)(102,340)(103,348)(104,347)
(105,346)(106,345)(107,344)(108,343)(109,351)(110,350)(111,349)(112,354)
(113,353)(114,352)(115,360)(116,359)(117,358)(118,357)(119,356)(120,355)
(121,369)(122,368)(123,367)(124,372)(125,371)(126,370)(127,363)(128,362)
(129,361)(130,366)(131,365)(132,364)(133,381)(134,380)(135,379)(136,384)
(137,383)(138,382)(139,375)(140,374)(141,373)(142,378)(143,377)(144,376)
(145,291)(146,290)(147,289)(148,294)(149,293)(150,292)(151,300)(152,299)
(153,298)(154,297)(155,296)(156,295)(157,303)(158,302)(159,301)(160,306)
(161,305)(162,304)(163,312)(164,311)(165,310)(166,309)(167,308)(168,307)
(169,321)(170,320)(171,319)(172,324)(173,323)(174,322)(175,315)(176,314)
(177,313)(178,318)(179,317)(180,316)(181,333)(182,332)(183,331)(184,336)
(185,335)(186,334)(187,327)(188,326)(189,325)(190,330)(191,329)(192,328);;
s2 := ( 7, 10)( 8, 11)( 9, 12)( 19, 22)( 20, 23)( 21, 24)( 25, 31)( 26, 32)
( 27, 33)( 28, 34)( 29, 35)( 30, 36)( 37, 43)( 38, 44)( 39, 45)( 40, 46)
( 41, 47)( 42, 48)( 55, 58)( 56, 59)( 57, 60)( 67, 70)( 68, 71)( 69, 72)
( 73, 79)( 74, 80)( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 85, 91)( 86, 92)
( 87, 93)( 88, 94)( 89, 95)( 90, 96)( 97,109)( 98,110)( 99,111)(100,112)
(101,113)(102,114)(103,118)(104,119)(105,120)(106,115)(107,116)(108,117)
(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(127,133)(128,134)
(129,135)(130,136)(131,137)(132,138)(145,157)(146,158)(147,159)(148,160)
(149,161)(150,162)(151,166)(152,167)(153,168)(154,163)(155,164)(156,165)
(169,187)(170,188)(171,189)(172,190)(173,191)(174,192)(175,181)(176,182)
(177,183)(178,184)(179,185)(180,186)(193,217)(194,218)(195,219)(196,220)
(197,221)(198,222)(199,226)(200,227)(201,228)(202,223)(203,224)(204,225)
(205,229)(206,230)(207,231)(208,232)(209,233)(210,234)(211,238)(212,239)
(213,240)(214,235)(215,236)(216,237)(241,265)(242,266)(243,267)(244,268)
(245,269)(246,270)(247,274)(248,275)(249,276)(250,271)(251,272)(252,273)
(253,277)(254,278)(255,279)(256,280)(257,281)(258,282)(259,286)(260,287)
(261,288)(262,283)(263,284)(264,285)(289,325)(290,326)(291,327)(292,328)
(293,329)(294,330)(295,334)(296,335)(297,336)(298,331)(299,332)(300,333)
(301,313)(302,314)(303,315)(304,316)(305,317)(306,318)(307,322)(308,323)
(309,324)(310,319)(311,320)(312,321)(337,373)(338,374)(339,375)(340,376)
(341,377)(342,378)(343,382)(344,383)(345,384)(346,379)(347,380)(348,381)
(349,361)(350,362)(351,363)(352,364)(353,365)(354,366)(355,370)(356,371)
(357,372)(358,367)(359,368)(360,369);;
s3 := ( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)
( 9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)( 16,112)
( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)( 24,120)
( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)
( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)( 48,144)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)
( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,159)( 64,160)
( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)( 72,168)
( 73,169)( 74,170)( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)( 80,176)
( 81,177)( 82,178)( 83,179)( 84,180)( 85,181)( 86,182)( 87,183)( 88,184)
( 89,185)( 90,186)( 91,187)( 92,188)( 93,189)( 94,190)( 95,191)( 96,192)
(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)(200,296)
(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)(208,304)
(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)(216,312)
(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)(224,320)
(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)(232,328)
(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)(240,336)
(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)(248,344)
(249,345)(250,346)(251,347)(252,348)(253,349)(254,350)(255,351)(256,352)
(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)
(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)(272,368)
(273,369)(274,370)(275,371)(276,372)(277,373)(278,374)(279,375)(280,376)
(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)(288,384);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1, 49)( 2, 51)( 3, 50)( 4, 52)( 5, 54)( 6, 53)( 7, 55)
( 8, 57)( 9, 56)( 10, 58)( 11, 60)( 12, 59)( 13, 61)( 14, 63)( 15, 62)
( 16, 64)( 17, 66)( 18, 65)( 19, 67)( 20, 69)( 21, 68)( 22, 70)( 23, 72)
( 24, 71)( 25, 73)( 26, 75)( 27, 74)( 28, 76)( 29, 78)( 30, 77)( 31, 79)
( 32, 81)( 33, 80)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 87)( 39, 86)
( 40, 88)( 41, 90)( 42, 89)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 96)
( 48, 95)( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,151)
(104,153)(105,152)(106,154)(107,156)(108,155)(109,157)(110,159)(111,158)
(112,160)(113,162)(114,161)(115,163)(116,165)(117,164)(118,166)(119,168)
(120,167)(121,169)(122,171)(123,170)(124,172)(125,174)(126,173)(127,175)
(128,177)(129,176)(130,178)(131,180)(132,179)(133,181)(134,183)(135,182)
(136,184)(137,186)(138,185)(139,187)(140,189)(141,188)(142,190)(143,192)
(144,191)(193,241)(194,243)(195,242)(196,244)(197,246)(198,245)(199,247)
(200,249)(201,248)(202,250)(203,252)(204,251)(205,253)(206,255)(207,254)
(208,256)(209,258)(210,257)(211,259)(212,261)(213,260)(214,262)(215,264)
(216,263)(217,265)(218,267)(219,266)(220,268)(221,270)(222,269)(223,271)
(224,273)(225,272)(226,274)(227,276)(228,275)(229,277)(230,279)(231,278)
(232,280)(233,282)(234,281)(235,283)(236,285)(237,284)(238,286)(239,288)
(240,287)(289,337)(290,339)(291,338)(292,340)(293,342)(294,341)(295,343)
(296,345)(297,344)(298,346)(299,348)(300,347)(301,349)(302,351)(303,350)
(304,352)(305,354)(306,353)(307,355)(308,357)(309,356)(310,358)(311,360)
(312,359)(313,361)(314,363)(315,362)(316,364)(317,366)(318,365)(319,367)
(320,369)(321,368)(322,370)(323,372)(324,371)(325,373)(326,375)(327,374)
(328,376)(329,378)(330,377)(331,379)(332,381)(333,380)(334,382)(335,384)
(336,383);
s1 := Sym(384)!( 1,243)( 2,242)( 3,241)( 4,246)( 5,245)( 6,244)( 7,252)
( 8,251)( 9,250)( 10,249)( 11,248)( 12,247)( 13,255)( 14,254)( 15,253)
( 16,258)( 17,257)( 18,256)( 19,264)( 20,263)( 21,262)( 22,261)( 23,260)
( 24,259)( 25,273)( 26,272)( 27,271)( 28,276)( 29,275)( 30,274)( 31,267)
( 32,266)( 33,265)( 34,270)( 35,269)( 36,268)( 37,285)( 38,284)( 39,283)
( 40,288)( 41,287)( 42,286)( 43,279)( 44,278)( 45,277)( 46,282)( 47,281)
( 48,280)( 49,195)( 50,194)( 51,193)( 52,198)( 53,197)( 54,196)( 55,204)
( 56,203)( 57,202)( 58,201)( 59,200)( 60,199)( 61,207)( 62,206)( 63,205)
( 64,210)( 65,209)( 66,208)( 67,216)( 68,215)( 69,214)( 70,213)( 71,212)
( 72,211)( 73,225)( 74,224)( 75,223)( 76,228)( 77,227)( 78,226)( 79,219)
( 80,218)( 81,217)( 82,222)( 83,221)( 84,220)( 85,237)( 86,236)( 87,235)
( 88,240)( 89,239)( 90,238)( 91,231)( 92,230)( 93,229)( 94,234)( 95,233)
( 96,232)( 97,339)( 98,338)( 99,337)(100,342)(101,341)(102,340)(103,348)
(104,347)(105,346)(106,345)(107,344)(108,343)(109,351)(110,350)(111,349)
(112,354)(113,353)(114,352)(115,360)(116,359)(117,358)(118,357)(119,356)
(120,355)(121,369)(122,368)(123,367)(124,372)(125,371)(126,370)(127,363)
(128,362)(129,361)(130,366)(131,365)(132,364)(133,381)(134,380)(135,379)
(136,384)(137,383)(138,382)(139,375)(140,374)(141,373)(142,378)(143,377)
(144,376)(145,291)(146,290)(147,289)(148,294)(149,293)(150,292)(151,300)
(152,299)(153,298)(154,297)(155,296)(156,295)(157,303)(158,302)(159,301)
(160,306)(161,305)(162,304)(163,312)(164,311)(165,310)(166,309)(167,308)
(168,307)(169,321)(170,320)(171,319)(172,324)(173,323)(174,322)(175,315)
(176,314)(177,313)(178,318)(179,317)(180,316)(181,333)(182,332)(183,331)
(184,336)(185,335)(186,334)(187,327)(188,326)(189,325)(190,330)(191,329)
(192,328);
s2 := Sym(384)!( 7, 10)( 8, 11)( 9, 12)( 19, 22)( 20, 23)( 21, 24)( 25, 31)
( 26, 32)( 27, 33)( 28, 34)( 29, 35)( 30, 36)( 37, 43)( 38, 44)( 39, 45)
( 40, 46)( 41, 47)( 42, 48)( 55, 58)( 56, 59)( 57, 60)( 67, 70)( 68, 71)
( 69, 72)( 73, 79)( 74, 80)( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 85, 91)
( 86, 92)( 87, 93)( 88, 94)( 89, 95)( 90, 96)( 97,109)( 98,110)( 99,111)
(100,112)(101,113)(102,114)(103,118)(104,119)(105,120)(106,115)(107,116)
(108,117)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(127,133)
(128,134)(129,135)(130,136)(131,137)(132,138)(145,157)(146,158)(147,159)
(148,160)(149,161)(150,162)(151,166)(152,167)(153,168)(154,163)(155,164)
(156,165)(169,187)(170,188)(171,189)(172,190)(173,191)(174,192)(175,181)
(176,182)(177,183)(178,184)(179,185)(180,186)(193,217)(194,218)(195,219)
(196,220)(197,221)(198,222)(199,226)(200,227)(201,228)(202,223)(203,224)
(204,225)(205,229)(206,230)(207,231)(208,232)(209,233)(210,234)(211,238)
(212,239)(213,240)(214,235)(215,236)(216,237)(241,265)(242,266)(243,267)
(244,268)(245,269)(246,270)(247,274)(248,275)(249,276)(250,271)(251,272)
(252,273)(253,277)(254,278)(255,279)(256,280)(257,281)(258,282)(259,286)
(260,287)(261,288)(262,283)(263,284)(264,285)(289,325)(290,326)(291,327)
(292,328)(293,329)(294,330)(295,334)(296,335)(297,336)(298,331)(299,332)
(300,333)(301,313)(302,314)(303,315)(304,316)(305,317)(306,318)(307,322)
(308,323)(309,324)(310,319)(311,320)(312,321)(337,373)(338,374)(339,375)
(340,376)(341,377)(342,378)(343,382)(344,383)(345,384)(346,379)(347,380)
(348,381)(349,361)(350,362)(351,363)(352,364)(353,365)(354,366)(355,370)
(356,371)(357,372)(358,367)(359,368)(360,369);
s3 := Sym(384)!( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)
( 8,104)( 9,105)( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,111)
( 16,112)( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)
( 24,120)( 25,121)( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)
( 32,128)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)
( 40,136)( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)
( 48,144)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)
( 56,152)( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,159)
( 64,160)( 65,161)( 66,162)( 67,163)( 68,164)( 69,165)( 70,166)( 71,167)
( 72,168)( 73,169)( 74,170)( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)
( 80,176)( 81,177)( 82,178)( 83,179)( 84,180)( 85,181)( 86,182)( 87,183)
( 88,184)( 89,185)( 90,186)( 91,187)( 92,188)( 93,189)( 94,190)( 95,191)
( 96,192)(193,289)(194,290)(195,291)(196,292)(197,293)(198,294)(199,295)
(200,296)(201,297)(202,298)(203,299)(204,300)(205,301)(206,302)(207,303)
(208,304)(209,305)(210,306)(211,307)(212,308)(213,309)(214,310)(215,311)
(216,312)(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)
(224,320)(225,321)(226,322)(227,323)(228,324)(229,325)(230,326)(231,327)
(232,328)(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)
(240,336)(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)
(248,344)(249,345)(250,346)(251,347)(252,348)(253,349)(254,350)(255,351)
(256,352)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)
(264,360)(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)
(272,368)(273,369)(274,370)(275,371)(276,372)(277,373)(278,374)(279,375)
(280,376)(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)
(288,384);
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*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope