Polytope of Type {8,10,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,10,10}*1600c
if this polytope has a name.
Group : SmallGroup(1600,8648)
Rank : 4
Schlafli Type : {8,10,10}
Number of vertices, edges, etc : 8, 40, 50, 10
Order of s0s1s2s3 : 40
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, {4,10,10}*800c
4-fold quotients : {4,10,5}*400, {2,10,10}*400b
5-fold quotients : {8,2,10}*320
8-fold quotients : {2,10,5}*200
10-fold quotients : {8,2,5}*160, {4,2,10}*160
20-fold quotients : {4,2,5}*80, {2,2,10}*80
25-fold quotients : {8,2,2}*64
40-fold quotients : {2,2,5}*40
50-fold quotients : {4,2,2}*32
100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,101)( 2,102)( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)( 8,108)
( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)
( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)
( 25,125)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)( 32,132)
( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)( 40,140)
( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)( 48,148)
( 49,149)( 50,150)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)( 56,181)
( 57,182)( 58,183)( 59,184)( 60,185)( 61,186)( 62,187)( 63,188)( 64,189)
( 65,190)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,196)( 72,197)
( 73,198)( 74,199)( 75,200)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)
( 81,156)( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)
( 89,164)( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)
( 97,172)( 98,173)( 99,174)(100,175)(201,301)(202,302)(203,303)(204,304)
(205,305)(206,306)(207,307)(208,308)(209,309)(210,310)(211,311)(212,312)
(213,313)(214,314)(215,315)(216,316)(217,317)(218,318)(219,319)(220,320)
(221,321)(222,322)(223,323)(224,324)(225,325)(226,326)(227,327)(228,328)
(229,329)(230,330)(231,331)(232,332)(233,333)(234,334)(235,335)(236,336)
(237,337)(238,338)(239,339)(240,340)(241,341)(242,342)(243,343)(244,344)
(245,345)(246,346)(247,347)(248,348)(249,349)(250,350)(251,376)(252,377)
(253,378)(254,379)(255,380)(256,381)(257,382)(258,383)(259,384)(260,385)
(261,386)(262,387)(263,388)(264,389)(265,390)(266,391)(267,392)(268,393)
(269,394)(270,395)(271,396)(272,397)(273,398)(274,399)(275,400)(276,351)
(277,352)(278,353)(279,354)(280,355)(281,356)(282,357)(283,358)(284,359)
(285,360)(286,361)(287,362)(288,363)(289,364)(290,365)(291,366)(292,367)
(293,368)(294,369)(295,370)(296,371)(297,372)(298,373)(299,374)(300,375);;
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)(206,221)
(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)(213,218)(214,219)
(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)(236,241)(237,242)
(238,243)(239,244)(240,245)(251,276)(252,277)(253,278)(254,279)(255,280)
(256,296)(257,297)(258,298)(259,299)(260,300)(261,291)(262,292)(263,293)
(264,294)(265,295)(266,286)(267,287)(268,288)(269,289)(270,290)(271,281)
(272,282)(273,283)(274,284)(275,285)(301,351)(302,352)(303,353)(304,354)
(305,355)(306,371)(307,372)(308,373)(309,374)(310,375)(311,366)(312,367)
(313,368)(314,369)(315,370)(316,361)(317,362)(318,363)(319,364)(320,365)
(321,356)(322,357)(323,358)(324,359)(325,360)(326,376)(327,377)(328,378)
(329,379)(330,380)(331,396)(332,397)(333,398)(334,399)(335,400)(336,391)
(337,392)(338,393)(339,394)(340,395)(341,386)(342,387)(343,388)(344,389)
(345,390)(346,381)(347,382)(348,383)(349,384)(350,385);;
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 := ( 1,202)( 2,201)( 3,205)( 4,204)( 5,203)( 6,222)( 7,221)( 8,225)
( 9,224)( 10,223)( 11,217)( 12,216)( 13,220)( 14,219)( 15,218)( 16,212)
( 17,211)( 18,215)( 19,214)( 20,213)( 21,207)( 22,206)( 23,210)( 24,209)
( 25,208)( 26,227)( 27,226)( 28,230)( 29,229)( 30,228)( 31,247)( 32,246)
( 33,250)( 34,249)( 35,248)( 36,242)( 37,241)( 38,245)( 39,244)( 40,243)
( 41,237)( 42,236)( 43,240)( 44,239)( 45,238)( 46,232)( 47,231)( 48,235)
( 49,234)( 50,233)( 51,252)( 52,251)( 53,255)( 54,254)( 55,253)( 56,272)
( 57,271)( 58,275)( 59,274)( 60,273)( 61,267)( 62,266)( 63,270)( 64,269)
( 65,268)( 66,262)( 67,261)( 68,265)( 69,264)( 70,263)( 71,257)( 72,256)
( 73,260)( 74,259)( 75,258)( 76,277)( 77,276)( 78,280)( 79,279)( 80,278)
( 81,297)( 82,296)( 83,300)( 84,299)( 85,298)( 86,292)( 87,291)( 88,295)
( 89,294)( 90,293)( 91,287)( 92,286)( 93,290)( 94,289)( 95,288)( 96,282)
( 97,281)( 98,285)( 99,284)(100,283)(101,302)(102,301)(103,305)(104,304)
(105,303)(106,322)(107,321)(108,325)(109,324)(110,323)(111,317)(112,316)
(113,320)(114,319)(115,318)(116,312)(117,311)(118,315)(119,314)(120,313)
(121,307)(122,306)(123,310)(124,309)(125,308)(126,327)(127,326)(128,330)
(129,329)(130,328)(131,347)(132,346)(133,350)(134,349)(135,348)(136,342)
(137,341)(138,345)(139,344)(140,343)(141,337)(142,336)(143,340)(144,339)
(145,338)(146,332)(147,331)(148,335)(149,334)(150,333)(151,352)(152,351)
(153,355)(154,354)(155,353)(156,372)(157,371)(158,375)(159,374)(160,373)
(161,367)(162,366)(163,370)(164,369)(165,368)(166,362)(167,361)(168,365)
(169,364)(170,363)(171,357)(172,356)(173,360)(174,359)(175,358)(176,377)
(177,376)(178,380)(179,379)(180,378)(181,397)(182,396)(183,400)(184,399)
(185,398)(186,392)(187,391)(188,395)(189,394)(190,393)(191,387)(192,386)
(193,390)(194,389)(195,388)(196,382)(197,381)(198,385)(199,384)(200,383);;
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, s0*s1*s0*s1*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,
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(400)!( 1,101)( 2,102)( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)
( 8,108)( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)
( 16,116)( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)
( 24,124)( 25,125)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)
( 32,132)( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)
( 40,140)( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)
( 48,148)( 49,149)( 50,150)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)
( 56,181)( 57,182)( 58,183)( 59,184)( 60,185)( 61,186)( 62,187)( 63,188)
( 64,189)( 65,190)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,196)
( 72,197)( 73,198)( 74,199)( 75,200)( 76,151)( 77,152)( 78,153)( 79,154)
( 80,155)( 81,156)( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)
( 88,163)( 89,164)( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)
( 96,171)( 97,172)( 98,173)( 99,174)(100,175)(201,301)(202,302)(203,303)
(204,304)(205,305)(206,306)(207,307)(208,308)(209,309)(210,310)(211,311)
(212,312)(213,313)(214,314)(215,315)(216,316)(217,317)(218,318)(219,319)
(220,320)(221,321)(222,322)(223,323)(224,324)(225,325)(226,326)(227,327)
(228,328)(229,329)(230,330)(231,331)(232,332)(233,333)(234,334)(235,335)
(236,336)(237,337)(238,338)(239,339)(240,340)(241,341)(242,342)(243,343)
(244,344)(245,345)(246,346)(247,347)(248,348)(249,349)(250,350)(251,376)
(252,377)(253,378)(254,379)(255,380)(256,381)(257,382)(258,383)(259,384)
(260,385)(261,386)(262,387)(263,388)(264,389)(265,390)(266,391)(267,392)
(268,393)(269,394)(270,395)(271,396)(272,397)(273,398)(274,399)(275,400)
(276,351)(277,352)(278,353)(279,354)(280,355)(281,356)(282,357)(283,358)
(284,359)(285,360)(286,361)(287,362)(288,363)(289,364)(290,365)(291,366)
(292,367)(293,368)(294,369)(295,370)(296,371)(297,372)(298,373)(299,374)
(300,375);
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)
(206,221)(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)(213,218)
(214,219)(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)(236,241)
(237,242)(238,243)(239,244)(240,245)(251,276)(252,277)(253,278)(254,279)
(255,280)(256,296)(257,297)(258,298)(259,299)(260,300)(261,291)(262,292)
(263,293)(264,294)(265,295)(266,286)(267,287)(268,288)(269,289)(270,290)
(271,281)(272,282)(273,283)(274,284)(275,285)(301,351)(302,352)(303,353)
(304,354)(305,355)(306,371)(307,372)(308,373)(309,374)(310,375)(311,366)
(312,367)(313,368)(314,369)(315,370)(316,361)(317,362)(318,363)(319,364)
(320,365)(321,356)(322,357)(323,358)(324,359)(325,360)(326,376)(327,377)
(328,378)(329,379)(330,380)(331,396)(332,397)(333,398)(334,399)(335,400)
(336,391)(337,392)(338,393)(339,394)(340,395)(341,386)(342,387)(343,388)
(344,389)(345,390)(346,381)(347,382)(348,383)(349,384)(350,385);
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)!( 1,202)( 2,201)( 3,205)( 4,204)( 5,203)( 6,222)( 7,221)
( 8,225)( 9,224)( 10,223)( 11,217)( 12,216)( 13,220)( 14,219)( 15,218)
( 16,212)( 17,211)( 18,215)( 19,214)( 20,213)( 21,207)( 22,206)( 23,210)
( 24,209)( 25,208)( 26,227)( 27,226)( 28,230)( 29,229)( 30,228)( 31,247)
( 32,246)( 33,250)( 34,249)( 35,248)( 36,242)( 37,241)( 38,245)( 39,244)
( 40,243)( 41,237)( 42,236)( 43,240)( 44,239)( 45,238)( 46,232)( 47,231)
( 48,235)( 49,234)( 50,233)( 51,252)( 52,251)( 53,255)( 54,254)( 55,253)
( 56,272)( 57,271)( 58,275)( 59,274)( 60,273)( 61,267)( 62,266)( 63,270)
( 64,269)( 65,268)( 66,262)( 67,261)( 68,265)( 69,264)( 70,263)( 71,257)
( 72,256)( 73,260)( 74,259)( 75,258)( 76,277)( 77,276)( 78,280)( 79,279)
( 80,278)( 81,297)( 82,296)( 83,300)( 84,299)( 85,298)( 86,292)( 87,291)
( 88,295)( 89,294)( 90,293)( 91,287)( 92,286)( 93,290)( 94,289)( 95,288)
( 96,282)( 97,281)( 98,285)( 99,284)(100,283)(101,302)(102,301)(103,305)
(104,304)(105,303)(106,322)(107,321)(108,325)(109,324)(110,323)(111,317)
(112,316)(113,320)(114,319)(115,318)(116,312)(117,311)(118,315)(119,314)
(120,313)(121,307)(122,306)(123,310)(124,309)(125,308)(126,327)(127,326)
(128,330)(129,329)(130,328)(131,347)(132,346)(133,350)(134,349)(135,348)
(136,342)(137,341)(138,345)(139,344)(140,343)(141,337)(142,336)(143,340)
(144,339)(145,338)(146,332)(147,331)(148,335)(149,334)(150,333)(151,352)
(152,351)(153,355)(154,354)(155,353)(156,372)(157,371)(158,375)(159,374)
(160,373)(161,367)(162,366)(163,370)(164,369)(165,368)(166,362)(167,361)
(168,365)(169,364)(170,363)(171,357)(172,356)(173,360)(174,359)(175,358)
(176,377)(177,376)(178,380)(179,379)(180,378)(181,397)(182,396)(183,400)
(184,399)(185,398)(186,392)(187,391)(188,395)(189,394)(190,393)(191,387)
(192,386)(193,390)(194,389)(195,388)(196,382)(197,381)(198,385)(199,384)
(200,383);
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,
s0*s1*s0*s1*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,
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