Polytope of Type {4,6,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,16}*768a
Also Known As : {{4,6|2},{6,16|2}}. if this polytope has another name.
Group : SmallGroup(768,326216)
Rank : 4
Schlafli Type : {4,6,16}
Number of vertices, edges, etc : 4, 12, 48, 16
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 : {4,6,8}*384a, {2,6,16}*384
3-fold quotients : {4,2,16}*256
4-fold quotients : {4,6,4}*192a, {2,6,8}*192
6-fold quotients : {4,2,8}*128, {2,2,16}*128
8-fold quotients : {2,6,4}*96a, {4,6,2}*96a
12-fold quotients : {4,2,4}*64, {2,2,8}*64
16-fold quotients : {2,6,2}*48
24-fold quotients : {2,2,4}*32, {4,2,2}*32
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, 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 := ( 1, 73)( 2, 75)( 3, 74)( 4, 76)( 5, 78)( 6, 77)( 7, 79)( 8, 81)
( 9, 80)( 10, 82)( 11, 84)( 12, 83)( 13, 85)( 14, 87)( 15, 86)( 16, 88)
( 17, 90)( 18, 89)( 19, 91)( 20, 93)( 21, 92)( 22, 94)( 23, 96)( 24, 95)
( 25, 58)( 26, 60)( 27, 59)( 28, 55)( 29, 57)( 30, 56)( 31, 49)( 32, 51)
( 33, 50)( 34, 52)( 35, 54)( 36, 53)( 37, 70)( 38, 72)( 39, 71)( 40, 67)
( 41, 69)( 42, 68)( 43, 61)( 44, 63)( 45, 62)( 46, 64)( 47, 66)( 48, 65)
( 97,181)( 98,183)( 99,182)(100,184)(101,186)(102,185)(103,187)(104,189)
(105,188)(106,190)(107,192)(108,191)(109,169)(110,171)(111,170)(112,172)
(113,174)(114,173)(115,175)(116,177)(117,176)(118,178)(119,180)(120,179)
(121,166)(122,168)(123,167)(124,163)(125,165)(126,164)(127,157)(128,159)
(129,158)(130,160)(131,162)(132,161)(133,154)(134,156)(135,155)(136,151)
(137,153)(138,152)(139,145)(140,147)(141,146)(142,148)(143,150)(144,149)
(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)
(289,349)(290,351)(291,350)(292,352)(293,354)(294,353)(295,355)(296,357)
(297,356)(298,358)(299,360)(300,359)(301,337)(302,339)(303,338)(304,340)
(305,342)(306,341)(307,343)(308,345)(309,344)(310,346)(311,348)(312,347)
(313,373)(314,375)(315,374)(316,376)(317,378)(318,377)(319,379)(320,381)
(321,380)(322,382)(323,384)(324,383)(325,361)(326,363)(327,362)(328,364)
(329,366)(330,365)(331,367)(332,369)(333,368)(334,370)(335,372)(336,371);;
s2 := ( 1, 60)( 2, 59)( 3, 58)( 4, 57)( 5, 56)( 6, 55)( 7, 54)( 8, 53)
( 9, 52)( 10, 51)( 11, 50)( 12, 49)( 13, 72)( 14, 71)( 15, 70)( 16, 69)
( 17, 68)( 18, 67)( 19, 66)( 20, 65)( 21, 64)( 22, 63)( 23, 62)( 24, 61)
( 25, 75)( 26, 74)( 27, 73)( 28, 78)( 29, 77)( 30, 76)( 31, 84)( 32, 83)
( 33, 82)( 34, 81)( 35, 80)( 36, 79)( 37, 87)( 38, 86)( 39, 85)( 40, 90)
( 41, 89)( 42, 88)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)( 48, 91)
( 97,156)( 98,155)( 99,154)(100,153)(101,152)(102,151)(103,150)(104,149)
(105,148)(106,147)(107,146)(108,145)(109,168)(110,167)(111,166)(112,165)
(113,164)(114,163)(115,162)(116,161)(117,160)(118,159)(119,158)(120,157)
(121,171)(122,170)(123,169)(124,174)(125,173)(126,172)(127,180)(128,179)
(129,178)(130,177)(131,176)(132,175)(133,183)(134,182)(135,181)(136,186)
(137,185)(138,184)(139,192)(140,191)(141,190)(142,189)(143,188)(144,187)
(193,252)(194,251)(195,250)(196,249)(197,248)(198,247)(199,246)(200,245)
(201,244)(202,243)(203,242)(204,241)(205,264)(206,263)(207,262)(208,261)
(209,260)(210,259)(211,258)(212,257)(213,256)(214,255)(215,254)(216,253)
(217,267)(218,266)(219,265)(220,270)(221,269)(222,268)(223,276)(224,275)
(225,274)(226,273)(227,272)(228,271)(229,279)(230,278)(231,277)(232,282)
(233,281)(234,280)(235,288)(236,287)(237,286)(238,285)(239,284)(240,283)
(289,348)(290,347)(291,346)(292,345)(293,344)(294,343)(295,342)(296,341)
(297,340)(298,339)(299,338)(300,337)(301,360)(302,359)(303,358)(304,357)
(305,356)(306,355)(307,354)(308,353)(309,352)(310,351)(311,350)(312,349)
(313,363)(314,362)(315,361)(316,366)(317,365)(318,364)(319,372)(320,371)
(321,370)(322,369)(323,368)(324,367)(325,375)(326,374)(327,373)(328,378)
(329,377)(330,376)(331,384)(332,383)(333,382)(334,381)(335,380)(336,379);;
s3 := ( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,202)( 8,203)
( 9,204)( 10,199)( 11,200)( 12,201)( 13,205)( 14,206)( 15,207)( 16,208)
( 17,209)( 18,210)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)( 24,213)
( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,217)( 32,218)
( 33,219)( 34,220)( 35,221)( 36,222)( 37,235)( 38,236)( 39,237)( 40,238)
( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)( 48,234)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,274)( 56,275)
( 57,276)( 58,271)( 59,272)( 60,273)( 61,277)( 62,278)( 63,279)( 64,280)
( 65,281)( 66,282)( 67,286)( 68,287)( 69,288)( 70,283)( 71,284)( 72,285)
( 73,241)( 74,242)( 75,243)( 76,244)( 77,245)( 78,246)( 79,250)( 80,251)
( 81,252)( 82,247)( 83,248)( 84,249)( 85,253)( 86,254)( 87,255)( 88,256)
( 89,257)( 90,258)( 91,262)( 92,263)( 93,264)( 94,259)( 95,260)( 96,261)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)(104,299)
(105,300)(106,295)(107,296)(108,297)(109,301)(110,302)(111,303)(112,304)
(113,305)(114,306)(115,310)(116,311)(117,312)(118,307)(119,308)(120,309)
(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,313)(128,314)
(129,315)(130,316)(131,317)(132,318)(133,331)(134,332)(135,333)(136,334)
(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)(144,330)
(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,370)(152,371)
(153,372)(154,367)(155,368)(156,369)(157,373)(158,374)(159,375)(160,376)
(161,377)(162,378)(163,382)(164,383)(165,384)(166,379)(167,380)(168,381)
(169,337)(170,338)(171,339)(172,340)(173,341)(174,342)(175,346)(176,347)
(177,348)(178,343)(179,344)(180,345)(181,349)(182,350)(183,351)(184,352)
(185,353)(186,354)(187,358)(188,359)(189,360)(190,355)(191,356)(192,357);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)!( 1, 73)( 2, 75)( 3, 74)( 4, 76)( 5, 78)( 6, 77)( 7, 79)
( 8, 81)( 9, 80)( 10, 82)( 11, 84)( 12, 83)( 13, 85)( 14, 87)( 15, 86)
( 16, 88)( 17, 90)( 18, 89)( 19, 91)( 20, 93)( 21, 92)( 22, 94)( 23, 96)
( 24, 95)( 25, 58)( 26, 60)( 27, 59)( 28, 55)( 29, 57)( 30, 56)( 31, 49)
( 32, 51)( 33, 50)( 34, 52)( 35, 54)( 36, 53)( 37, 70)( 38, 72)( 39, 71)
( 40, 67)( 41, 69)( 42, 68)( 43, 61)( 44, 63)( 45, 62)( 46, 64)( 47, 66)
( 48, 65)( 97,181)( 98,183)( 99,182)(100,184)(101,186)(102,185)(103,187)
(104,189)(105,188)(106,190)(107,192)(108,191)(109,169)(110,171)(111,170)
(112,172)(113,174)(114,173)(115,175)(116,177)(117,176)(118,178)(119,180)
(120,179)(121,166)(122,168)(123,167)(124,163)(125,165)(126,164)(127,157)
(128,159)(129,158)(130,160)(131,162)(132,161)(133,154)(134,156)(135,155)
(136,151)(137,153)(138,152)(139,145)(140,147)(141,146)(142,148)(143,150)
(144,149)(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)(289,349)(290,351)(291,350)(292,352)(293,354)(294,353)(295,355)
(296,357)(297,356)(298,358)(299,360)(300,359)(301,337)(302,339)(303,338)
(304,340)(305,342)(306,341)(307,343)(308,345)(309,344)(310,346)(311,348)
(312,347)(313,373)(314,375)(315,374)(316,376)(317,378)(318,377)(319,379)
(320,381)(321,380)(322,382)(323,384)(324,383)(325,361)(326,363)(327,362)
(328,364)(329,366)(330,365)(331,367)(332,369)(333,368)(334,370)(335,372)
(336,371);
s2 := Sym(384)!( 1, 60)( 2, 59)( 3, 58)( 4, 57)( 5, 56)( 6, 55)( 7, 54)
( 8, 53)( 9, 52)( 10, 51)( 11, 50)( 12, 49)( 13, 72)( 14, 71)( 15, 70)
( 16, 69)( 17, 68)( 18, 67)( 19, 66)( 20, 65)( 21, 64)( 22, 63)( 23, 62)
( 24, 61)( 25, 75)( 26, 74)( 27, 73)( 28, 78)( 29, 77)( 30, 76)( 31, 84)
( 32, 83)( 33, 82)( 34, 81)( 35, 80)( 36, 79)( 37, 87)( 38, 86)( 39, 85)
( 40, 90)( 41, 89)( 42, 88)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)
( 48, 91)( 97,156)( 98,155)( 99,154)(100,153)(101,152)(102,151)(103,150)
(104,149)(105,148)(106,147)(107,146)(108,145)(109,168)(110,167)(111,166)
(112,165)(113,164)(114,163)(115,162)(116,161)(117,160)(118,159)(119,158)
(120,157)(121,171)(122,170)(123,169)(124,174)(125,173)(126,172)(127,180)
(128,179)(129,178)(130,177)(131,176)(132,175)(133,183)(134,182)(135,181)
(136,186)(137,185)(138,184)(139,192)(140,191)(141,190)(142,189)(143,188)
(144,187)(193,252)(194,251)(195,250)(196,249)(197,248)(198,247)(199,246)
(200,245)(201,244)(202,243)(203,242)(204,241)(205,264)(206,263)(207,262)
(208,261)(209,260)(210,259)(211,258)(212,257)(213,256)(214,255)(215,254)
(216,253)(217,267)(218,266)(219,265)(220,270)(221,269)(222,268)(223,276)
(224,275)(225,274)(226,273)(227,272)(228,271)(229,279)(230,278)(231,277)
(232,282)(233,281)(234,280)(235,288)(236,287)(237,286)(238,285)(239,284)
(240,283)(289,348)(290,347)(291,346)(292,345)(293,344)(294,343)(295,342)
(296,341)(297,340)(298,339)(299,338)(300,337)(301,360)(302,359)(303,358)
(304,357)(305,356)(306,355)(307,354)(308,353)(309,352)(310,351)(311,350)
(312,349)(313,363)(314,362)(315,361)(316,366)(317,365)(318,364)(319,372)
(320,371)(321,370)(322,369)(323,368)(324,367)(325,375)(326,374)(327,373)
(328,378)(329,377)(330,376)(331,384)(332,383)(333,382)(334,381)(335,380)
(336,379);
s3 := Sym(384)!( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,202)
( 8,203)( 9,204)( 10,199)( 11,200)( 12,201)( 13,205)( 14,206)( 15,207)
( 16,208)( 17,209)( 18,210)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)
( 24,213)( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,217)
( 32,218)( 33,219)( 34,220)( 35,221)( 36,222)( 37,235)( 38,236)( 39,237)
( 40,238)( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)
( 48,234)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,274)
( 56,275)( 57,276)( 58,271)( 59,272)( 60,273)( 61,277)( 62,278)( 63,279)
( 64,280)( 65,281)( 66,282)( 67,286)( 68,287)( 69,288)( 70,283)( 71,284)
( 72,285)( 73,241)( 74,242)( 75,243)( 76,244)( 77,245)( 78,246)( 79,250)
( 80,251)( 81,252)( 82,247)( 83,248)( 84,249)( 85,253)( 86,254)( 87,255)
( 88,256)( 89,257)( 90,258)( 91,262)( 92,263)( 93,264)( 94,259)( 95,260)
( 96,261)( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)
(104,299)(105,300)(106,295)(107,296)(108,297)(109,301)(110,302)(111,303)
(112,304)(113,305)(114,306)(115,310)(116,311)(117,312)(118,307)(119,308)
(120,309)(121,319)(122,320)(123,321)(124,322)(125,323)(126,324)(127,313)
(128,314)(129,315)(130,316)(131,317)(132,318)(133,331)(134,332)(135,333)
(136,334)(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)
(144,330)(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,370)
(152,371)(153,372)(154,367)(155,368)(156,369)(157,373)(158,374)(159,375)
(160,376)(161,377)(162,378)(163,382)(164,383)(165,384)(166,379)(167,380)
(168,381)(169,337)(170,338)(171,339)(172,340)(173,341)(174,342)(175,346)
(176,347)(177,348)(178,343)(179,344)(180,345)(181,349)(182,350)(183,351)
(184,352)(185,353)(186,354)(187,358)(188,359)(189,360)(190,355)(191,356)
(192,357);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope