Polytope of Type {16,10,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,10,5}*1600
if this polytope has a name.
Group : SmallGroup(1600,3558)
Rank : 4
Schlafli Type : {16,10,5}
Number of vertices, edges, etc : 16, 80, 25, 5
Order of s0s1s2s3 : 80
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 : {8,10,5}*800
4-fold quotients : {4,10,5}*400
5-fold quotients : {16,2,5}*320
8-fold quotients : {2,10,5}*200
10-fold quotients : {8,2,5}*160
20-fold quotients : {4,2,5}*80
40-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,201)( 2,202)( 3,203)( 4,204)( 5,205)( 6,206)( 7,207)( 8,208)
( 9,209)( 10,210)( 11,211)( 12,212)( 13,213)( 14,214)( 15,215)( 16,216)
( 17,217)( 18,218)( 19,219)( 20,220)( 21,221)( 22,222)( 23,223)( 24,224)
( 25,225)( 26,226)( 27,227)( 28,228)( 29,229)( 30,230)( 31,231)( 32,232)
( 33,233)( 34,234)( 35,235)( 36,236)( 37,237)( 38,238)( 39,239)( 40,240)
( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,246)( 47,247)( 48,248)
( 49,249)( 50,250)( 51,276)( 52,277)( 53,278)( 54,279)( 55,280)( 56,281)
( 57,282)( 58,283)( 59,284)( 60,285)( 61,286)( 62,287)( 63,288)( 64,289)
( 65,290)( 66,291)( 67,292)( 68,293)( 69,294)( 70,295)( 71,296)( 72,297)
( 73,298)( 74,299)( 75,300)( 76,251)( 77,252)( 78,253)( 79,254)( 80,255)
( 81,256)( 82,257)( 83,258)( 84,259)( 85,260)( 86,261)( 87,262)( 88,263)
( 89,264)( 90,265)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)( 96,271)
( 97,272)( 98,273)( 99,274)(100,275)(101,351)(102,352)(103,353)(104,354)
(105,355)(106,356)(107,357)(108,358)(109,359)(110,360)(111,361)(112,362)
(113,363)(114,364)(115,365)(116,366)(117,367)(118,368)(119,369)(120,370)
(121,371)(122,372)(123,373)(124,374)(125,375)(126,376)(127,377)(128,378)
(129,379)(130,380)(131,381)(132,382)(133,383)(134,384)(135,385)(136,386)
(137,387)(138,388)(139,389)(140,390)(141,391)(142,392)(143,393)(144,394)
(145,395)(146,396)(147,397)(148,398)(149,399)(150,400)(151,301)(152,302)
(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)(160,310)
(161,311)(162,312)(163,313)(164,314)(165,315)(166,316)(167,317)(168,318)
(169,319)(170,320)(171,321)(172,322)(173,323)(174,324)(175,325)(176,326)
(177,327)(178,328)(179,329)(180,330)(181,331)(182,332)(183,333)(184,334)
(185,335)(186,336)(187,337)(188,338)(189,339)(190,340)(191,341)(192,342)
(193,343)(194,344)(195,345)(196,346)(197,347)(198,348)(199,349)(200,350);;
s1 := ( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)( 54, 79)
( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)( 62, 92)
( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)
( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(101,151)(102,152)(103,153)
(104,154)(105,155)(106,171)(107,172)(108,173)(109,174)(110,175)(111,166)
(112,167)(113,168)(114,169)(115,170)(116,161)(117,162)(118,163)(119,164)
(120,165)(121,156)(122,157)(123,158)(124,159)(125,160)(126,176)(127,177)
(128,178)(129,179)(130,180)(131,196)(132,197)(133,198)(134,199)(135,200)
(136,191)(137,192)(138,193)(139,194)(140,195)(141,186)(142,187)(143,188)
(144,189)(145,190)(146,181)(147,182)(148,183)(149,184)(150,185)(201,301)
(202,302)(203,303)(204,304)(205,305)(206,321)(207,322)(208,323)(209,324)
(210,325)(211,316)(212,317)(213,318)(214,319)(215,320)(216,311)(217,312)
(218,313)(219,314)(220,315)(221,306)(222,307)(223,308)(224,309)(225,310)
(226,326)(227,327)(228,328)(229,329)(230,330)(231,346)(232,347)(233,348)
(234,349)(235,350)(236,341)(237,342)(238,343)(239,344)(240,345)(241,336)
(242,337)(243,338)(244,339)(245,340)(246,331)(247,332)(248,333)(249,334)
(250,335)(251,376)(252,377)(253,378)(254,379)(255,380)(256,396)(257,397)
(258,398)(259,399)(260,400)(261,391)(262,392)(263,393)(264,394)(265,395)
(266,386)(267,387)(268,388)(269,389)(270,390)(271,381)(272,382)(273,383)
(274,384)(275,385)(276,351)(277,352)(278,353)(279,354)(280,355)(281,371)
(282,372)(283,373)(284,374)(285,375)(286,366)(287,367)(288,368)(289,369)
(290,370)(291,361)(292,362)(293,363)(294,364)(295,365)(296,356)(297,357)
(298,358)(299,359)(300,360);;
s2 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 21)( 12, 25)( 13, 24)
( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26, 31)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 36, 46)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 42, 45)( 43, 44)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 71)( 62, 75)( 63, 74)
( 64, 73)( 65, 72)( 67, 70)( 68, 69)( 76, 81)( 77, 85)( 78, 84)( 79, 83)
( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 92, 95)( 93, 94)
(101,106)(102,110)(103,109)(104,108)(105,107)(111,121)(112,125)(113,124)
(114,123)(115,122)(117,120)(118,119)(126,131)(127,135)(128,134)(129,133)
(130,132)(136,146)(137,150)(138,149)(139,148)(140,147)(142,145)(143,144)
(151,156)(152,160)(153,159)(154,158)(155,157)(161,171)(162,175)(163,174)
(164,173)(165,172)(167,170)(168,169)(176,181)(177,185)(178,184)(179,183)
(180,182)(186,196)(187,200)(188,199)(189,198)(190,197)(192,195)(193,194)
(201,206)(202,210)(203,209)(204,208)(205,207)(211,221)(212,225)(213,224)
(214,223)(215,222)(217,220)(218,219)(226,231)(227,235)(228,234)(229,233)
(230,232)(236,246)(237,250)(238,249)(239,248)(240,247)(242,245)(243,244)
(251,256)(252,260)(253,259)(254,258)(255,257)(261,271)(262,275)(263,274)
(264,273)(265,272)(267,270)(268,269)(276,281)(277,285)(278,284)(279,283)
(280,282)(286,296)(287,300)(288,299)(289,298)(290,297)(292,295)(293,294)
(301,306)(302,310)(303,309)(304,308)(305,307)(311,321)(312,325)(313,324)
(314,323)(315,322)(317,320)(318,319)(326,331)(327,335)(328,334)(329,333)
(330,332)(336,346)(337,350)(338,349)(339,348)(340,347)(342,345)(343,344)
(351,356)(352,360)(353,359)(354,358)(355,357)(361,371)(362,375)(363,374)
(364,373)(365,372)(367,370)(368,369)(376,381)(377,385)(378,384)(379,383)
(380,382)(386,396)(387,400)(388,399)(389,398)(390,397)(392,395)(393,394);;
s3 := ( 1, 2)( 3, 5)( 6, 22)( 7, 21)( 8, 25)( 9, 24)( 10, 23)( 11, 17)
( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 27)( 28, 30)( 31, 47)( 32, 46)
( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)
( 51, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)( 61, 67)
( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76, 77)( 78, 80)( 81, 97)( 82, 96)
( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)( 90, 93)
(101,102)(103,105)(106,122)(107,121)(108,125)(109,124)(110,123)(111,117)
(112,116)(113,120)(114,119)(115,118)(126,127)(128,130)(131,147)(132,146)
(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)(139,144)(140,143)
(151,152)(153,155)(156,172)(157,171)(158,175)(159,174)(160,173)(161,167)
(162,166)(163,170)(164,169)(165,168)(176,177)(178,180)(181,197)(182,196)
(183,200)(184,199)(185,198)(186,192)(187,191)(188,195)(189,194)(190,193)
(201,202)(203,205)(206,222)(207,221)(208,225)(209,224)(210,223)(211,217)
(212,216)(213,220)(214,219)(215,218)(226,227)(228,230)(231,247)(232,246)
(233,250)(234,249)(235,248)(236,242)(237,241)(238,245)(239,244)(240,243)
(251,252)(253,255)(256,272)(257,271)(258,275)(259,274)(260,273)(261,267)
(262,266)(263,270)(264,269)(265,268)(276,277)(278,280)(281,297)(282,296)
(283,300)(284,299)(285,298)(286,292)(287,291)(288,295)(289,294)(290,293)
(301,302)(303,305)(306,322)(307,321)(308,325)(309,324)(310,323)(311,317)
(312,316)(313,320)(314,319)(315,318)(326,327)(328,330)(331,347)(332,346)
(333,350)(334,349)(335,348)(336,342)(337,341)(338,345)(339,344)(340,343)
(351,352)(353,355)(356,372)(357,371)(358,375)(359,374)(360,373)(361,367)
(362,366)(363,370)(364,369)(365,368)(376,377)(378,380)(381,397)(382,396)
(383,400)(384,399)(385,398)(386,392)(387,391)(388,395)(389,394)(390,393);;
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,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(400)!( 1,201)( 2,202)( 3,203)( 4,204)( 5,205)( 6,206)( 7,207)
( 8,208)( 9,209)( 10,210)( 11,211)( 12,212)( 13,213)( 14,214)( 15,215)
( 16,216)( 17,217)( 18,218)( 19,219)( 20,220)( 21,221)( 22,222)( 23,223)
( 24,224)( 25,225)( 26,226)( 27,227)( 28,228)( 29,229)( 30,230)( 31,231)
( 32,232)( 33,233)( 34,234)( 35,235)( 36,236)( 37,237)( 38,238)( 39,239)
( 40,240)( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,246)( 47,247)
( 48,248)( 49,249)( 50,250)( 51,276)( 52,277)( 53,278)( 54,279)( 55,280)
( 56,281)( 57,282)( 58,283)( 59,284)( 60,285)( 61,286)( 62,287)( 63,288)
( 64,289)( 65,290)( 66,291)( 67,292)( 68,293)( 69,294)( 70,295)( 71,296)
( 72,297)( 73,298)( 74,299)( 75,300)( 76,251)( 77,252)( 78,253)( 79,254)
( 80,255)( 81,256)( 82,257)( 83,258)( 84,259)( 85,260)( 86,261)( 87,262)
( 88,263)( 89,264)( 90,265)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)
( 96,271)( 97,272)( 98,273)( 99,274)(100,275)(101,351)(102,352)(103,353)
(104,354)(105,355)(106,356)(107,357)(108,358)(109,359)(110,360)(111,361)
(112,362)(113,363)(114,364)(115,365)(116,366)(117,367)(118,368)(119,369)
(120,370)(121,371)(122,372)(123,373)(124,374)(125,375)(126,376)(127,377)
(128,378)(129,379)(130,380)(131,381)(132,382)(133,383)(134,384)(135,385)
(136,386)(137,387)(138,388)(139,389)(140,390)(141,391)(142,392)(143,393)
(144,394)(145,395)(146,396)(147,397)(148,398)(149,399)(150,400)(151,301)
(152,302)(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)
(160,310)(161,311)(162,312)(163,313)(164,314)(165,315)(166,316)(167,317)
(168,318)(169,319)(170,320)(171,321)(172,322)(173,323)(174,324)(175,325)
(176,326)(177,327)(178,328)(179,329)(180,330)(181,331)(182,332)(183,333)
(184,334)(185,335)(186,336)(187,337)(188,338)(189,339)(190,340)(191,341)
(192,342)(193,343)(194,344)(195,345)(196,346)(197,347)(198,348)(199,349)
(200,350);
s1 := Sym(400)!( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)
( 54, 79)( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)
( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)
( 70, 90)( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(101,151)(102,152)
(103,153)(104,154)(105,155)(106,171)(107,172)(108,173)(109,174)(110,175)
(111,166)(112,167)(113,168)(114,169)(115,170)(116,161)(117,162)(118,163)
(119,164)(120,165)(121,156)(122,157)(123,158)(124,159)(125,160)(126,176)
(127,177)(128,178)(129,179)(130,180)(131,196)(132,197)(133,198)(134,199)
(135,200)(136,191)(137,192)(138,193)(139,194)(140,195)(141,186)(142,187)
(143,188)(144,189)(145,190)(146,181)(147,182)(148,183)(149,184)(150,185)
(201,301)(202,302)(203,303)(204,304)(205,305)(206,321)(207,322)(208,323)
(209,324)(210,325)(211,316)(212,317)(213,318)(214,319)(215,320)(216,311)
(217,312)(218,313)(219,314)(220,315)(221,306)(222,307)(223,308)(224,309)
(225,310)(226,326)(227,327)(228,328)(229,329)(230,330)(231,346)(232,347)
(233,348)(234,349)(235,350)(236,341)(237,342)(238,343)(239,344)(240,345)
(241,336)(242,337)(243,338)(244,339)(245,340)(246,331)(247,332)(248,333)
(249,334)(250,335)(251,376)(252,377)(253,378)(254,379)(255,380)(256,396)
(257,397)(258,398)(259,399)(260,400)(261,391)(262,392)(263,393)(264,394)
(265,395)(266,386)(267,387)(268,388)(269,389)(270,390)(271,381)(272,382)
(273,383)(274,384)(275,385)(276,351)(277,352)(278,353)(279,354)(280,355)
(281,371)(282,372)(283,373)(284,374)(285,375)(286,366)(287,367)(288,368)
(289,369)(290,370)(291,361)(292,362)(293,363)(294,364)(295,365)(296,356)
(297,357)(298,358)(299,359)(300,360);
s2 := Sym(400)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 21)( 12, 25)
( 13, 24)( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26, 31)( 27, 35)( 28, 34)
( 29, 33)( 30, 32)( 36, 46)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 42, 45)
( 43, 44)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 71)( 62, 75)
( 63, 74)( 64, 73)( 65, 72)( 67, 70)( 68, 69)( 76, 81)( 77, 85)( 78, 84)
( 79, 83)( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 92, 95)
( 93, 94)(101,106)(102,110)(103,109)(104,108)(105,107)(111,121)(112,125)
(113,124)(114,123)(115,122)(117,120)(118,119)(126,131)(127,135)(128,134)
(129,133)(130,132)(136,146)(137,150)(138,149)(139,148)(140,147)(142,145)
(143,144)(151,156)(152,160)(153,159)(154,158)(155,157)(161,171)(162,175)
(163,174)(164,173)(165,172)(167,170)(168,169)(176,181)(177,185)(178,184)
(179,183)(180,182)(186,196)(187,200)(188,199)(189,198)(190,197)(192,195)
(193,194)(201,206)(202,210)(203,209)(204,208)(205,207)(211,221)(212,225)
(213,224)(214,223)(215,222)(217,220)(218,219)(226,231)(227,235)(228,234)
(229,233)(230,232)(236,246)(237,250)(238,249)(239,248)(240,247)(242,245)
(243,244)(251,256)(252,260)(253,259)(254,258)(255,257)(261,271)(262,275)
(263,274)(264,273)(265,272)(267,270)(268,269)(276,281)(277,285)(278,284)
(279,283)(280,282)(286,296)(287,300)(288,299)(289,298)(290,297)(292,295)
(293,294)(301,306)(302,310)(303,309)(304,308)(305,307)(311,321)(312,325)
(313,324)(314,323)(315,322)(317,320)(318,319)(326,331)(327,335)(328,334)
(329,333)(330,332)(336,346)(337,350)(338,349)(339,348)(340,347)(342,345)
(343,344)(351,356)(352,360)(353,359)(354,358)(355,357)(361,371)(362,375)
(363,374)(364,373)(365,372)(367,370)(368,369)(376,381)(377,385)(378,384)
(379,383)(380,382)(386,396)(387,400)(388,399)(389,398)(390,397)(392,395)
(393,394);
s3 := Sym(400)!( 1, 2)( 3, 5)( 6, 22)( 7, 21)( 8, 25)( 9, 24)( 10, 23)
( 11, 17)( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 27)( 28, 30)( 31, 47)
( 32, 46)( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)
( 40, 43)( 51, 52)( 53, 55)( 56, 72)( 57, 71)( 58, 75)( 59, 74)( 60, 73)
( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 76, 77)( 78, 80)( 81, 97)
( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)
( 90, 93)(101,102)(103,105)(106,122)(107,121)(108,125)(109,124)(110,123)
(111,117)(112,116)(113,120)(114,119)(115,118)(126,127)(128,130)(131,147)
(132,146)(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)(139,144)
(140,143)(151,152)(153,155)(156,172)(157,171)(158,175)(159,174)(160,173)
(161,167)(162,166)(163,170)(164,169)(165,168)(176,177)(178,180)(181,197)
(182,196)(183,200)(184,199)(185,198)(186,192)(187,191)(188,195)(189,194)
(190,193)(201,202)(203,205)(206,222)(207,221)(208,225)(209,224)(210,223)
(211,217)(212,216)(213,220)(214,219)(215,218)(226,227)(228,230)(231,247)
(232,246)(233,250)(234,249)(235,248)(236,242)(237,241)(238,245)(239,244)
(240,243)(251,252)(253,255)(256,272)(257,271)(258,275)(259,274)(260,273)
(261,267)(262,266)(263,270)(264,269)(265,268)(276,277)(278,280)(281,297)
(282,296)(283,300)(284,299)(285,298)(286,292)(287,291)(288,295)(289,294)
(290,293)(301,302)(303,305)(306,322)(307,321)(308,325)(309,324)(310,323)
(311,317)(312,316)(313,320)(314,319)(315,318)(326,327)(328,330)(331,347)
(332,346)(333,350)(334,349)(335,348)(336,342)(337,341)(338,345)(339,344)
(340,343)(351,352)(353,355)(356,372)(357,371)(358,375)(359,374)(360,373)
(361,367)(362,366)(363,370)(364,369)(365,368)(376,377)(378,380)(381,397)
(382,396)(383,400)(384,399)(385,398)(386,392)(387,391)(388,395)(389,394)
(390,393);
poly := sub<Sym(400)|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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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