Polytope of Type {4,16,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,16,6}*768a
Also Known As : {{4,16|2},{16,6|2}}. if this polytope has another name.
Group : SmallGroup(768,323301)
Rank : 4
Schlafli Type : {4,16,6}
Number of vertices, edges, etc : 4, 32, 48, 6
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 : {4,8,6}*384a, {2,16,6}*384
3-fold quotients : {4,16,2}*256a
4-fold quotients : {4,4,6}*192, {2,8,6}*192
6-fold quotients : {4,8,2}*128a, {2,16,2}*128
8-fold quotients : {2,4,6}*96a, {4,2,6}*96
12-fold quotients : {4,4,2}*64, {2,8,2}*64
16-fold quotients : {4,2,3}*48, {2,2,6}*48
24-fold quotients : {2,4,2}*32, {4,2,2}*32
32-fold quotients : {2,2,3}*24
48-fold quotients : {2,2,2}*16
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)
( 9,105)( 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);;
s1 := ( 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);;
s2 := ( 1,241)( 2,243)( 3,242)( 4,244)( 5,246)( 6,245)( 7,250)( 8,252)
( 9,251)( 10,247)( 11,249)( 12,248)( 13,253)( 14,255)( 15,254)( 16,256)
( 17,258)( 18,257)( 19,262)( 20,264)( 21,263)( 22,259)( 23,261)( 24,260)
( 25,271)( 26,273)( 27,272)( 28,274)( 29,276)( 30,275)( 31,265)( 32,267)
( 33,266)( 34,268)( 35,270)( 36,269)( 37,283)( 38,285)( 39,284)( 40,286)
( 41,288)( 42,287)( 43,277)( 44,279)( 45,278)( 46,280)( 47,282)( 48,281)
( 49,193)( 50,195)( 51,194)( 52,196)( 53,198)( 54,197)( 55,202)( 56,204)
( 57,203)( 58,199)( 59,201)( 60,200)( 61,205)( 62,207)( 63,206)( 64,208)
( 65,210)( 66,209)( 67,214)( 68,216)( 69,215)( 70,211)( 71,213)( 72,212)
( 73,223)( 74,225)( 75,224)( 76,226)( 77,228)( 78,227)( 79,217)( 80,219)
( 81,218)( 82,220)( 83,222)( 84,221)( 85,235)( 86,237)( 87,236)( 88,238)
( 89,240)( 90,239)( 91,229)( 92,231)( 93,230)( 94,232)( 95,234)( 96,233)
( 97,337)( 98,339)( 99,338)(100,340)(101,342)(102,341)(103,346)(104,348)
(105,347)(106,343)(107,345)(108,344)(109,349)(110,351)(111,350)(112,352)
(113,354)(114,353)(115,358)(116,360)(117,359)(118,355)(119,357)(120,356)
(121,367)(122,369)(123,368)(124,370)(125,372)(126,371)(127,361)(128,363)
(129,362)(130,364)(131,366)(132,365)(133,379)(134,381)(135,380)(136,382)
(137,384)(138,383)(139,373)(140,375)(141,374)(142,376)(143,378)(144,377)
(145,289)(146,291)(147,290)(148,292)(149,294)(150,293)(151,298)(152,300)
(153,299)(154,295)(155,297)(156,296)(157,301)(158,303)(159,302)(160,304)
(161,306)(162,305)(163,310)(164,312)(165,311)(166,307)(167,309)(168,308)
(169,319)(170,321)(171,320)(172,322)(173,324)(174,323)(175,313)(176,315)
(177,314)(178,316)(179,318)(180,317)(181,331)(182,333)(183,332)(184,334)
(185,336)(186,335)(187,325)(188,327)(189,326)(190,328)(191,330)(192,329);;
s3 := ( 1, 51)( 2, 50)( 3, 49)( 4, 54)( 5, 53)( 6, 52)( 7, 57)( 8, 56)
( 9, 55)( 10, 60)( 11, 59)( 12, 58)( 13, 63)( 14, 62)( 15, 61)( 16, 66)
( 17, 65)( 18, 64)( 19, 69)( 20, 68)( 21, 67)( 22, 72)( 23, 71)( 24, 70)
( 25, 75)( 26, 74)( 27, 73)( 28, 78)( 29, 77)( 30, 76)( 31, 81)( 32, 80)
( 33, 79)( 34, 84)( 35, 83)( 36, 82)( 37, 87)( 38, 86)( 39, 85)( 40, 90)
( 41, 89)( 42, 88)( 43, 93)( 44, 92)( 45, 91)( 46, 96)( 47, 95)( 48, 94)
( 97,147)( 98,146)( 99,145)(100,150)(101,149)(102,148)(103,153)(104,152)
(105,151)(106,156)(107,155)(108,154)(109,159)(110,158)(111,157)(112,162)
(113,161)(114,160)(115,165)(116,164)(117,163)(118,168)(119,167)(120,166)
(121,171)(122,170)(123,169)(124,174)(125,173)(126,172)(127,177)(128,176)
(129,175)(130,180)(131,179)(132,178)(133,183)(134,182)(135,181)(136,186)
(137,185)(138,184)(139,189)(140,188)(141,187)(142,192)(143,191)(144,190)
(193,243)(194,242)(195,241)(196,246)(197,245)(198,244)(199,249)(200,248)
(201,247)(202,252)(203,251)(204,250)(205,255)(206,254)(207,253)(208,258)
(209,257)(210,256)(211,261)(212,260)(213,259)(214,264)(215,263)(216,262)
(217,267)(218,266)(219,265)(220,270)(221,269)(222,268)(223,273)(224,272)
(225,271)(226,276)(227,275)(228,274)(229,279)(230,278)(231,277)(232,282)
(233,281)(234,280)(235,285)(236,284)(237,283)(238,288)(239,287)(240,286)
(289,339)(290,338)(291,337)(292,342)(293,341)(294,340)(295,345)(296,344)
(297,343)(298,348)(299,347)(300,346)(301,351)(302,350)(303,349)(304,354)
(305,353)(306,352)(307,357)(308,356)(309,355)(310,360)(311,359)(312,358)
(313,363)(314,362)(315,361)(316,366)(317,365)(318,364)(319,369)(320,368)
(321,367)(322,372)(323,371)(324,370)(325,375)(326,374)(327,373)(328,378)
(329,377)(330,376)(331,381)(332,380)(333,379)(334,384)(335,383)(336,382);;
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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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, 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);
s1 := 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);
s2 := Sym(384)!( 1,241)( 2,243)( 3,242)( 4,244)( 5,246)( 6,245)( 7,250)
( 8,252)( 9,251)( 10,247)( 11,249)( 12,248)( 13,253)( 14,255)( 15,254)
( 16,256)( 17,258)( 18,257)( 19,262)( 20,264)( 21,263)( 22,259)( 23,261)
( 24,260)( 25,271)( 26,273)( 27,272)( 28,274)( 29,276)( 30,275)( 31,265)
( 32,267)( 33,266)( 34,268)( 35,270)( 36,269)( 37,283)( 38,285)( 39,284)
( 40,286)( 41,288)( 42,287)( 43,277)( 44,279)( 45,278)( 46,280)( 47,282)
( 48,281)( 49,193)( 50,195)( 51,194)( 52,196)( 53,198)( 54,197)( 55,202)
( 56,204)( 57,203)( 58,199)( 59,201)( 60,200)( 61,205)( 62,207)( 63,206)
( 64,208)( 65,210)( 66,209)( 67,214)( 68,216)( 69,215)( 70,211)( 71,213)
( 72,212)( 73,223)( 74,225)( 75,224)( 76,226)( 77,228)( 78,227)( 79,217)
( 80,219)( 81,218)( 82,220)( 83,222)( 84,221)( 85,235)( 86,237)( 87,236)
( 88,238)( 89,240)( 90,239)( 91,229)( 92,231)( 93,230)( 94,232)( 95,234)
( 96,233)( 97,337)( 98,339)( 99,338)(100,340)(101,342)(102,341)(103,346)
(104,348)(105,347)(106,343)(107,345)(108,344)(109,349)(110,351)(111,350)
(112,352)(113,354)(114,353)(115,358)(116,360)(117,359)(118,355)(119,357)
(120,356)(121,367)(122,369)(123,368)(124,370)(125,372)(126,371)(127,361)
(128,363)(129,362)(130,364)(131,366)(132,365)(133,379)(134,381)(135,380)
(136,382)(137,384)(138,383)(139,373)(140,375)(141,374)(142,376)(143,378)
(144,377)(145,289)(146,291)(147,290)(148,292)(149,294)(150,293)(151,298)
(152,300)(153,299)(154,295)(155,297)(156,296)(157,301)(158,303)(159,302)
(160,304)(161,306)(162,305)(163,310)(164,312)(165,311)(166,307)(167,309)
(168,308)(169,319)(170,321)(171,320)(172,322)(173,324)(174,323)(175,313)
(176,315)(177,314)(178,316)(179,318)(180,317)(181,331)(182,333)(183,332)
(184,334)(185,336)(186,335)(187,325)(188,327)(189,326)(190,328)(191,330)
(192,329);
s3 := Sym(384)!( 1, 51)( 2, 50)( 3, 49)( 4, 54)( 5, 53)( 6, 52)( 7, 57)
( 8, 56)( 9, 55)( 10, 60)( 11, 59)( 12, 58)( 13, 63)( 14, 62)( 15, 61)
( 16, 66)( 17, 65)( 18, 64)( 19, 69)( 20, 68)( 21, 67)( 22, 72)( 23, 71)
( 24, 70)( 25, 75)( 26, 74)( 27, 73)( 28, 78)( 29, 77)( 30, 76)( 31, 81)
( 32, 80)( 33, 79)( 34, 84)( 35, 83)( 36, 82)( 37, 87)( 38, 86)( 39, 85)
( 40, 90)( 41, 89)( 42, 88)( 43, 93)( 44, 92)( 45, 91)( 46, 96)( 47, 95)
( 48, 94)( 97,147)( 98,146)( 99,145)(100,150)(101,149)(102,148)(103,153)
(104,152)(105,151)(106,156)(107,155)(108,154)(109,159)(110,158)(111,157)
(112,162)(113,161)(114,160)(115,165)(116,164)(117,163)(118,168)(119,167)
(120,166)(121,171)(122,170)(123,169)(124,174)(125,173)(126,172)(127,177)
(128,176)(129,175)(130,180)(131,179)(132,178)(133,183)(134,182)(135,181)
(136,186)(137,185)(138,184)(139,189)(140,188)(141,187)(142,192)(143,191)
(144,190)(193,243)(194,242)(195,241)(196,246)(197,245)(198,244)(199,249)
(200,248)(201,247)(202,252)(203,251)(204,250)(205,255)(206,254)(207,253)
(208,258)(209,257)(210,256)(211,261)(212,260)(213,259)(214,264)(215,263)
(216,262)(217,267)(218,266)(219,265)(220,270)(221,269)(222,268)(223,273)
(224,272)(225,271)(226,276)(227,275)(228,274)(229,279)(230,278)(231,277)
(232,282)(233,281)(234,280)(235,285)(236,284)(237,283)(238,288)(239,287)
(240,286)(289,339)(290,338)(291,337)(292,342)(293,341)(294,340)(295,345)
(296,344)(297,343)(298,348)(299,347)(300,346)(301,351)(302,350)(303,349)
(304,354)(305,353)(306,352)(307,357)(308,356)(309,355)(310,360)(311,359)
(312,358)(313,363)(314,362)(315,361)(316,366)(317,365)(318,364)(319,369)
(320,368)(321,367)(322,372)(323,371)(324,370)(325,375)(326,374)(327,373)
(328,378)(329,377)(330,376)(331,381)(332,380)(333,379)(334,384)(335,383)
(336,382);
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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