Polytope of Type {100,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {100,8}*1600a
Also Known As : {100,8|2}. if this polytope has another name.
Group : SmallGroup(1600,401)
Rank : 3
Schlafli Type : {100,8}
Number of vertices, edges, etc : 100, 400, 8
Order of s₀s₁s₂ : 200
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {100,4}*800, {50,8}*800
   4-fold quotients : {100,2}*400, {50,4}*400
   5-fold quotients : {20,8}*320a
   8-fold quotients : {50,2}*200
   10-fold quotients : {20,4}*160, {10,8}*160
   16-fold quotients : {25,2}*100
   20-fold quotients : {20,2}*80, {10,4}*80
   25-fold quotients : {4,8}*64a
   40-fold quotients : {10,2}*40
   50-fold quotients : {4,4}*32, {2,8}*32
   80-fold quotients : {5,2}*20
   100-fold quotients : {2,4}*16, {4,2}*16
   200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  5)(  3,  4)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)( 11, 20)
( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)( 32, 49)
( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)
( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)( 61, 70)
( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)( 82, 99)
( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)( 90, 91)
(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)(110,121)(111,120)
(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)(131,150)(132,149)
(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)(140,141)
(152,155)(153,154)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)
(162,169)(163,168)(164,167)(165,166)(177,180)(178,179)(181,200)(182,199)
(183,198)(184,197)(185,196)(186,195)(187,194)(188,193)(189,192)(190,191)
(201,251)(202,255)(203,254)(204,253)(205,252)(206,275)(207,274)(208,273)
(209,272)(210,271)(211,270)(212,269)(213,268)(214,267)(215,266)(216,265)
(217,264)(218,263)(219,262)(220,261)(221,260)(222,259)(223,258)(224,257)
(225,256)(226,276)(227,280)(228,279)(229,278)(230,277)(231,300)(232,299)
(233,298)(234,297)(235,296)(236,295)(237,294)(238,293)(239,292)(240,291)
(241,290)(242,289)(243,288)(244,287)(245,286)(246,285)(247,284)(248,283)
(249,282)(250,281)(301,351)(302,355)(303,354)(304,353)(305,352)(306,375)
(307,374)(308,373)(309,372)(310,371)(311,370)(312,369)(313,368)(314,367)
(315,366)(316,365)(317,364)(318,363)(319,362)(320,361)(321,360)(322,359)
(323,358)(324,357)(325,356)(326,376)(327,380)(328,379)(329,378)(330,377)
(331,400)(332,399)(333,398)(334,397)(335,396)(336,395)(337,394)(338,393)
(339,392)(340,391)(341,390)(342,389)(343,388)(344,387)(345,386)(346,385)
(347,384)(348,383)(349,382)(350,381);;
s1 := (  1,206)(  2,210)(  3,209)(  4,208)(  5,207)(  6,201)(  7,205)(  8,204)
(  9,203)( 10,202)( 11,225)( 12,224)( 13,223)( 14,222)( 15,221)( 16,220)
( 17,219)( 18,218)( 19,217)( 20,216)( 21,215)( 22,214)( 23,213)( 24,212)
( 25,211)( 26,231)( 27,235)( 28,234)( 29,233)( 30,232)( 31,226)( 32,230)
( 33,229)( 34,228)( 35,227)( 36,250)( 37,249)( 38,248)( 39,247)( 40,246)
( 41,245)( 42,244)( 43,243)( 44,242)( 45,241)( 46,240)( 47,239)( 48,238)
( 49,237)( 50,236)( 51,256)( 52,260)( 53,259)( 54,258)( 55,257)( 56,251)
( 57,255)( 58,254)( 59,253)( 60,252)( 61,275)( 62,274)( 63,273)( 64,272)
( 65,271)( 66,270)( 67,269)( 68,268)( 69,267)( 70,266)( 71,265)( 72,264)
( 73,263)( 74,262)( 75,261)( 76,281)( 77,285)( 78,284)( 79,283)( 80,282)
( 81,276)( 82,280)( 83,279)( 84,278)( 85,277)( 86,300)( 87,299)( 88,298)
( 89,297)( 90,296)( 91,295)( 92,294)( 93,293)( 94,292)( 95,291)( 96,290)
( 97,289)( 98,288)( 99,287)(100,286)(101,331)(102,335)(103,334)(104,333)
(105,332)(106,326)(107,330)(108,329)(109,328)(110,327)(111,350)(112,349)
(113,348)(114,347)(115,346)(116,345)(117,344)(118,343)(119,342)(120,341)
(121,340)(122,339)(123,338)(124,337)(125,336)(126,306)(127,310)(128,309)
(129,308)(130,307)(131,301)(132,305)(133,304)(134,303)(135,302)(136,325)
(137,324)(138,323)(139,322)(140,321)(141,320)(142,319)(143,318)(144,317)
(145,316)(146,315)(147,314)(148,313)(149,312)(150,311)(151,381)(152,385)
(153,384)(154,383)(155,382)(156,376)(157,380)(158,379)(159,378)(160,377)
(161,400)(162,399)(163,398)(164,397)(165,396)(166,395)(167,394)(168,393)
(169,392)(170,391)(171,390)(172,389)(173,388)(174,387)(175,386)(176,356)
(177,360)(178,359)(179,358)(180,357)(181,351)(182,355)(183,354)(184,353)
(185,352)(186,375)(187,374)(188,373)(189,372)(190,371)(191,370)(192,369)
(193,368)(194,367)(195,366)(196,365)(197,364)(198,363)(199,362)(200,361);;
s2 := (101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)(108,133)
(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)(115,140)(116,141)
(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)(123,148)(124,149)
(125,150)(151,176)(152,177)(153,178)(154,179)(155,180)(156,181)(157,182)
(158,183)(159,184)(160,185)(161,186)(162,187)(163,188)(164,189)(165,190)
(166,191)(167,192)(168,193)(169,194)(170,195)(171,196)(172,197)(173,198)
(174,199)(175,200)(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)(251,351)(252,352)(253,353)(254,354)
(255,355)(256,356)(257,357)(258,358)(259,359)(260,360)(261,361)(262,362)
(263,363)(264,364)(265,365)(266,366)(267,367)(268,368)(269,369)(270,370)
(271,371)(272,372)(273,373)(274,374)(275,375)(276,376)(277,377)(278,378)
(279,379)(280,380)(281,381)(282,382)(283,383)(284,384)(285,385)(286,386)
(287,387)(288,388)(289,389)(290,390)(291,391)(292,392)(293,393)(294,394)
(295,395)(296,396)(297,397)(298,398)(299,399)(300,400);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*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*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*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*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*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*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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(400)!(  2,  5)(  3,  4)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)
( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)
( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)
( 40, 41)( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)
( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)
( 82, 99)( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)
( 90, 91)(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)(110,121)
(111,120)(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)(131,150)
(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)
(140,141)(152,155)(153,154)(156,175)(157,174)(158,173)(159,172)(160,171)
(161,170)(162,169)(163,168)(164,167)(165,166)(177,180)(178,179)(181,200)
(182,199)(183,198)(184,197)(185,196)(186,195)(187,194)(188,193)(189,192)
(190,191)(201,251)(202,255)(203,254)(204,253)(205,252)(206,275)(207,274)
(208,273)(209,272)(210,271)(211,270)(212,269)(213,268)(214,267)(215,266)
(216,265)(217,264)(218,263)(219,262)(220,261)(221,260)(222,259)(223,258)
(224,257)(225,256)(226,276)(227,280)(228,279)(229,278)(230,277)(231,300)
(232,299)(233,298)(234,297)(235,296)(236,295)(237,294)(238,293)(239,292)
(240,291)(241,290)(242,289)(243,288)(244,287)(245,286)(246,285)(247,284)
(248,283)(249,282)(250,281)(301,351)(302,355)(303,354)(304,353)(305,352)
(306,375)(307,374)(308,373)(309,372)(310,371)(311,370)(312,369)(313,368)
(314,367)(315,366)(316,365)(317,364)(318,363)(319,362)(320,361)(321,360)
(322,359)(323,358)(324,357)(325,356)(326,376)(327,380)(328,379)(329,378)
(330,377)(331,400)(332,399)(333,398)(334,397)(335,396)(336,395)(337,394)
(338,393)(339,392)(340,391)(341,390)(342,389)(343,388)(344,387)(345,386)
(346,385)(347,384)(348,383)(349,382)(350,381);
s1 := Sym(400)!(  1,206)(  2,210)(  3,209)(  4,208)(  5,207)(  6,201)(  7,205)
(  8,204)(  9,203)( 10,202)( 11,225)( 12,224)( 13,223)( 14,222)( 15,221)
( 16,220)( 17,219)( 18,218)( 19,217)( 20,216)( 21,215)( 22,214)( 23,213)
( 24,212)( 25,211)( 26,231)( 27,235)( 28,234)( 29,233)( 30,232)( 31,226)
( 32,230)( 33,229)( 34,228)( 35,227)( 36,250)( 37,249)( 38,248)( 39,247)
( 40,246)( 41,245)( 42,244)( 43,243)( 44,242)( 45,241)( 46,240)( 47,239)
( 48,238)( 49,237)( 50,236)( 51,256)( 52,260)( 53,259)( 54,258)( 55,257)
( 56,251)( 57,255)( 58,254)( 59,253)( 60,252)( 61,275)( 62,274)( 63,273)
( 64,272)( 65,271)( 66,270)( 67,269)( 68,268)( 69,267)( 70,266)( 71,265)
( 72,264)( 73,263)( 74,262)( 75,261)( 76,281)( 77,285)( 78,284)( 79,283)
( 80,282)( 81,276)( 82,280)( 83,279)( 84,278)( 85,277)( 86,300)( 87,299)
( 88,298)( 89,297)( 90,296)( 91,295)( 92,294)( 93,293)( 94,292)( 95,291)
( 96,290)( 97,289)( 98,288)( 99,287)(100,286)(101,331)(102,335)(103,334)
(104,333)(105,332)(106,326)(107,330)(108,329)(109,328)(110,327)(111,350)
(112,349)(113,348)(114,347)(115,346)(116,345)(117,344)(118,343)(119,342)
(120,341)(121,340)(122,339)(123,338)(124,337)(125,336)(126,306)(127,310)
(128,309)(129,308)(130,307)(131,301)(132,305)(133,304)(134,303)(135,302)
(136,325)(137,324)(138,323)(139,322)(140,321)(141,320)(142,319)(143,318)
(144,317)(145,316)(146,315)(147,314)(148,313)(149,312)(150,311)(151,381)
(152,385)(153,384)(154,383)(155,382)(156,376)(157,380)(158,379)(159,378)
(160,377)(161,400)(162,399)(163,398)(164,397)(165,396)(166,395)(167,394)
(168,393)(169,392)(170,391)(171,390)(172,389)(173,388)(174,387)(175,386)
(176,356)(177,360)(178,359)(179,358)(180,357)(181,351)(182,355)(183,354)
(184,353)(185,352)(186,375)(187,374)(188,373)(189,372)(190,371)(191,370)
(192,369)(193,368)(194,367)(195,366)(196,365)(197,364)(198,363)(199,362)
(200,361);
s2 := Sym(400)!(101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)
(108,133)(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)(115,140)
(116,141)(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)(123,148)
(124,149)(125,150)(151,176)(152,177)(153,178)(154,179)(155,180)(156,181)
(157,182)(158,183)(159,184)(160,185)(161,186)(162,187)(163,188)(164,189)
(165,190)(166,191)(167,192)(168,193)(169,194)(170,195)(171,196)(172,197)
(173,198)(174,199)(175,200)(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)(251,351)(252,352)(253,353)
(254,354)(255,355)(256,356)(257,357)(258,358)(259,359)(260,360)(261,361)
(262,362)(263,363)(264,364)(265,365)(266,366)(267,367)(268,368)(269,369)
(270,370)(271,371)(272,372)(273,373)(274,374)(275,375)(276,376)(277,377)
(278,378)(279,379)(280,380)(281,381)(282,382)(283,383)(284,384)(285,385)
(286,386)(287,387)(288,388)(289,389)(290,390)(291,391)(292,392)(293,393)
(294,394)(295,395)(296,396)(297,397)(298,398)(299,399)(300,400);
poly := sub<Sym(400)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*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*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*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*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*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*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*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope