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Polytope of Type {16,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,6,4}*768a
Also Known As : {{16,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(768,326216)
Rank : 4
Schlafli Type : {16,6,4}
Number of vertices, edges, etc : 16, 48, 12, 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 : {8,6,4}*384a, {16,6,2}*384
   3-fold quotients : {16,2,4}*256
   4-fold quotients : {4,6,4}*192a, {8,6,2}*192
   6-fold quotients : {8,2,4}*128, {16,2,2}*128
   8-fold quotients : {2,6,4}*96a, {4,6,2}*96a
   12-fold quotients : {4,2,4}*64, {8,2,2}*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 := (  1,193)(  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);;
s1 := (  1, 49)(  2, 51)(  3, 50)(  4, 52)(  5, 54)(  6, 53)(  7, 58)(  8, 60)
(  9, 59)( 10, 55)( 11, 57)( 12, 56)( 13, 61)( 14, 63)( 15, 62)( 16, 64)
( 17, 66)( 18, 65)( 19, 70)( 20, 72)( 21, 71)( 22, 67)( 23, 69)( 24, 68)
( 25, 79)( 26, 81)( 27, 80)( 28, 82)( 29, 84)( 30, 83)( 31, 73)( 32, 75)
( 33, 74)( 34, 76)( 35, 78)( 36, 77)( 37, 91)( 38, 93)( 39, 92)( 40, 94)
( 41, 96)( 42, 95)( 43, 85)( 44, 87)( 45, 86)( 46, 88)( 47, 90)( 48, 89)
( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,154)(104,156)
(105,155)(106,151)(107,153)(108,152)(109,157)(110,159)(111,158)(112,160)
(113,162)(114,161)(115,166)(116,168)(117,167)(118,163)(119,165)(120,164)
(121,175)(122,177)(123,176)(124,178)(125,180)(126,179)(127,169)(128,171)
(129,170)(130,172)(131,174)(132,173)(133,187)(134,189)(135,188)(136,190)
(137,192)(138,191)(139,181)(140,183)(141,182)(142,184)(143,186)(144,185)
(193,241)(194,243)(195,242)(196,244)(197,246)(198,245)(199,250)(200,252)
(201,251)(202,247)(203,249)(204,248)(205,253)(206,255)(207,254)(208,256)
(209,258)(210,257)(211,262)(212,264)(213,263)(214,259)(215,261)(216,260)
(217,271)(218,273)(219,272)(220,274)(221,276)(222,275)(223,265)(224,267)
(225,266)(226,268)(227,270)(228,269)(229,283)(230,285)(231,284)(232,286)
(233,288)(234,287)(235,277)(236,279)(237,278)(238,280)(239,282)(240,281)
(289,337)(290,339)(291,338)(292,340)(293,342)(294,341)(295,346)(296,348)
(297,347)(298,343)(299,345)(300,344)(301,349)(302,351)(303,350)(304,352)
(305,354)(306,353)(307,358)(308,360)(309,359)(310,355)(311,357)(312,356)
(313,367)(314,369)(315,368)(316,370)(317,372)(318,371)(319,361)(320,363)
(321,362)(322,364)(323,366)(324,365)(325,379)(326,381)(327,380)(328,382)
(329,384)(330,383)(331,373)(332,375)(333,374)(334,376)(335,378)(336,377);;
s2 := (  1, 75)(  2, 74)(  3, 73)(  4, 78)(  5, 77)(  6, 76)(  7, 81)(  8, 80)
(  9, 79)( 10, 84)( 11, 83)( 12, 82)( 13, 87)( 14, 86)( 15, 85)( 16, 90)
( 17, 89)( 18, 88)( 19, 93)( 20, 92)( 21, 91)( 22, 96)( 23, 95)( 24, 94)
( 25, 60)( 26, 59)( 27, 58)( 28, 57)( 29, 56)( 30, 55)( 31, 51)( 32, 50)
( 33, 49)( 34, 54)( 35, 53)( 36, 52)( 37, 72)( 38, 71)( 39, 70)( 40, 69)
( 41, 68)( 42, 67)( 43, 63)( 44, 62)( 45, 61)( 46, 66)( 47, 65)( 48, 64)
( 97,183)( 98,182)( 99,181)(100,186)(101,185)(102,184)(103,189)(104,188)
(105,187)(106,192)(107,191)(108,190)(109,171)(110,170)(111,169)(112,174)
(113,173)(114,172)(115,177)(116,176)(117,175)(118,180)(119,179)(120,178)
(121,168)(122,167)(123,166)(124,165)(125,164)(126,163)(127,159)(128,158)
(129,157)(130,162)(131,161)(132,160)(133,156)(134,155)(135,154)(136,153)
(137,152)(138,151)(139,147)(140,146)(141,145)(142,150)(143,149)(144,148)
(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)
(289,351)(290,350)(291,349)(292,354)(293,353)(294,352)(295,357)(296,356)
(297,355)(298,360)(299,359)(300,358)(301,339)(302,338)(303,337)(304,342)
(305,341)(306,340)(307,345)(308,344)(309,343)(310,348)(311,347)(312,346)
(313,375)(314,374)(315,373)(316,378)(317,377)(318,376)(319,381)(320,380)
(321,379)(322,384)(323,383)(324,382)(325,363)(326,362)(327,361)(328,366)
(329,365)(330,364)(331,369)(332,368)(333,367)(334,372)(335,371)(336,370);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(384)!(  1, 49)(  2, 51)(  3, 50)(  4, 52)(  5, 54)(  6, 53)(  7, 58)
(  8, 60)(  9, 59)( 10, 55)( 11, 57)( 12, 56)( 13, 61)( 14, 63)( 15, 62)
( 16, 64)( 17, 66)( 18, 65)( 19, 70)( 20, 72)( 21, 71)( 22, 67)( 23, 69)
( 24, 68)( 25, 79)( 26, 81)( 27, 80)( 28, 82)( 29, 84)( 30, 83)( 31, 73)
( 32, 75)( 33, 74)( 34, 76)( 35, 78)( 36, 77)( 37, 91)( 38, 93)( 39, 92)
( 40, 94)( 41, 96)( 42, 95)( 43, 85)( 44, 87)( 45, 86)( 46, 88)( 47, 90)
( 48, 89)( 97,145)( 98,147)( 99,146)(100,148)(101,150)(102,149)(103,154)
(104,156)(105,155)(106,151)(107,153)(108,152)(109,157)(110,159)(111,158)
(112,160)(113,162)(114,161)(115,166)(116,168)(117,167)(118,163)(119,165)
(120,164)(121,175)(122,177)(123,176)(124,178)(125,180)(126,179)(127,169)
(128,171)(129,170)(130,172)(131,174)(132,173)(133,187)(134,189)(135,188)
(136,190)(137,192)(138,191)(139,181)(140,183)(141,182)(142,184)(143,186)
(144,185)(193,241)(194,243)(195,242)(196,244)(197,246)(198,245)(199,250)
(200,252)(201,251)(202,247)(203,249)(204,248)(205,253)(206,255)(207,254)
(208,256)(209,258)(210,257)(211,262)(212,264)(213,263)(214,259)(215,261)
(216,260)(217,271)(218,273)(219,272)(220,274)(221,276)(222,275)(223,265)
(224,267)(225,266)(226,268)(227,270)(228,269)(229,283)(230,285)(231,284)
(232,286)(233,288)(234,287)(235,277)(236,279)(237,278)(238,280)(239,282)
(240,281)(289,337)(290,339)(291,338)(292,340)(293,342)(294,341)(295,346)
(296,348)(297,347)(298,343)(299,345)(300,344)(301,349)(302,351)(303,350)
(304,352)(305,354)(306,353)(307,358)(308,360)(309,359)(310,355)(311,357)
(312,356)(313,367)(314,369)(315,368)(316,370)(317,372)(318,371)(319,361)
(320,363)(321,362)(322,364)(323,366)(324,365)(325,379)(326,381)(327,380)
(328,382)(329,384)(330,383)(331,373)(332,375)(333,374)(334,376)(335,378)
(336,377);
s2 := Sym(384)!(  1, 75)(  2, 74)(  3, 73)(  4, 78)(  5, 77)(  6, 76)(  7, 81)
(  8, 80)(  9, 79)( 10, 84)( 11, 83)( 12, 82)( 13, 87)( 14, 86)( 15, 85)
( 16, 90)( 17, 89)( 18, 88)( 19, 93)( 20, 92)( 21, 91)( 22, 96)( 23, 95)
( 24, 94)( 25, 60)( 26, 59)( 27, 58)( 28, 57)( 29, 56)( 30, 55)( 31, 51)
( 32, 50)( 33, 49)( 34, 54)( 35, 53)( 36, 52)( 37, 72)( 38, 71)( 39, 70)
( 40, 69)( 41, 68)( 42, 67)( 43, 63)( 44, 62)( 45, 61)( 46, 66)( 47, 65)
( 48, 64)( 97,183)( 98,182)( 99,181)(100,186)(101,185)(102,184)(103,189)
(104,188)(105,187)(106,192)(107,191)(108,190)(109,171)(110,170)(111,169)
(112,174)(113,173)(114,172)(115,177)(116,176)(117,175)(118,180)(119,179)
(120,178)(121,168)(122,167)(123,166)(124,165)(125,164)(126,163)(127,159)
(128,158)(129,157)(130,162)(131,161)(132,160)(133,156)(134,155)(135,154)
(136,153)(137,152)(138,151)(139,147)(140,146)(141,145)(142,150)(143,149)
(144,148)(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)(289,351)(290,350)(291,349)(292,354)(293,353)(294,352)(295,357)
(296,356)(297,355)(298,360)(299,359)(300,358)(301,339)(302,338)(303,337)
(304,342)(305,341)(306,340)(307,345)(308,344)(309,343)(310,348)(311,347)
(312,346)(313,375)(314,374)(315,373)(316,378)(317,377)(318,376)(319,381)
(320,380)(321,379)(322,384)(323,383)(324,382)(325,363)(326,362)(327,361)
(328,366)(329,365)(330,364)(331,369)(332,368)(333,367)(334,372)(335,371)
(336,370);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope