Polytope of Type {2,8,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,4,10}*1280b
if this polytope has a name.
Group : SmallGroup(1280,1036167)
Rank : 5
Schlafli Type : {2,8,4,10}
Number of vertices, edges, etc : 2, 8, 16, 20, 10
Order of s0s1s2s3s4 : 40
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,4,4,10}*640
4-fold quotients : {2,2,4,10}*320, {2,4,2,10}*320
5-fold quotients : {2,8,4,2}*256b
8-fold quotients : {2,4,2,5}*160, {2,2,2,10}*160
10-fold quotients : {2,4,4,2}*128
16-fold quotients : {2,2,2,5}*80
20-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)( 8,168)( 9,169)( 10,170)
( 11,171)( 12,172)( 13,178)( 14,179)( 15,180)( 16,181)( 17,182)( 18,173)
( 19,174)( 20,175)( 21,176)( 22,177)( 23,188)( 24,189)( 25,190)( 26,191)
( 27,192)( 28,183)( 29,184)( 30,185)( 31,186)( 32,187)( 33,193)( 34,194)
( 35,195)( 36,196)( 37,197)( 38,198)( 39,199)( 40,200)( 41,201)( 42,202)
( 43,203)( 44,204)( 45,205)( 46,206)( 47,207)( 48,208)( 49,209)( 50,210)
( 51,211)( 52,212)( 53,218)( 54,219)( 55,220)( 56,221)( 57,222)( 58,213)
( 59,214)( 60,215)( 61,216)( 62,217)( 63,228)( 64,229)( 65,230)( 66,231)
( 67,232)( 68,223)( 69,224)( 70,225)( 71,226)( 72,227)( 73,233)( 74,234)
( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)( 80,240)( 81,241)( 82,242)
( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)( 88,248)( 89,249)( 90,250)
( 91,251)( 92,252)( 93,258)( 94,259)( 95,260)( 96,261)( 97,262)( 98,253)
( 99,254)(100,255)(101,256)(102,257)(103,268)(104,269)(105,270)(106,271)
(107,272)(108,263)(109,264)(110,265)(111,266)(112,267)(113,273)(114,274)
(115,275)(116,276)(117,277)(118,278)(119,279)(120,280)(121,281)(122,282)
(123,283)(124,284)(125,285)(126,286)(127,287)(128,288)(129,289)(130,290)
(131,291)(132,292)(133,298)(134,299)(135,300)(136,301)(137,302)(138,293)
(139,294)(140,295)(141,296)(142,297)(143,308)(144,309)(145,310)(146,311)
(147,312)(148,303)(149,304)(150,305)(151,306)(152,307)(153,313)(154,314)
(155,315)(156,316)(157,317)(158,318)(159,319)(160,320)(161,321)(162,322);;
s2 := ( 23, 28)( 24, 29)( 25, 30)( 26, 31)( 27, 32)( 33, 38)( 34, 39)( 35, 40)
( 36, 41)( 37, 42)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)( 73, 78)
( 74, 79)( 75, 80)( 76, 81)( 77, 82)( 83, 93)( 84, 94)( 85, 95)( 86, 96)
( 87, 97)( 88, 98)( 89, 99)( 90,100)( 91,101)( 92,102)(103,118)(104,119)
(105,120)(106,121)(107,122)(108,113)(109,114)(110,115)(111,116)(112,117)
(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)(130,140)
(131,141)(132,142)(143,158)(144,159)(145,160)(146,161)(147,162)(148,153)
(149,154)(150,155)(151,156)(152,157)(163,183)(164,184)(165,185)(166,186)
(167,187)(168,188)(169,189)(170,190)(171,191)(172,192)(173,193)(174,194)
(175,195)(176,196)(177,197)(178,198)(179,199)(180,200)(181,201)(182,202)
(203,223)(204,224)(205,225)(206,226)(207,227)(208,228)(209,229)(210,230)
(211,231)(212,232)(213,233)(214,234)(215,235)(216,236)(217,237)(218,238)
(219,239)(220,240)(221,241)(222,242)(243,278)(244,279)(245,280)(246,281)
(247,282)(248,273)(249,274)(250,275)(251,276)(252,277)(253,268)(254,269)
(255,270)(256,271)(257,272)(258,263)(259,264)(260,265)(261,266)(262,267)
(283,318)(284,319)(285,320)(286,321)(287,322)(288,313)(289,314)(290,315)
(291,316)(292,317)(293,308)(294,309)(295,310)(296,311)(297,312)(298,303)
(299,304)(300,305)(301,306)(302,307);;
s3 := ( 3,123)( 4,127)( 5,126)( 6,125)( 7,124)( 8,128)( 9,132)( 10,131)
( 11,130)( 12,129)( 13,133)( 14,137)( 15,136)( 16,135)( 17,134)( 18,138)
( 19,142)( 20,141)( 21,140)( 22,139)( 23,148)( 24,152)( 25,151)( 26,150)
( 27,149)( 28,143)( 29,147)( 30,146)( 31,145)( 32,144)( 33,158)( 34,162)
( 35,161)( 36,160)( 37,159)( 38,153)( 39,157)( 40,156)( 41,155)( 42,154)
( 43, 83)( 44, 87)( 45, 86)( 46, 85)( 47, 84)( 48, 88)( 49, 92)( 50, 91)
( 51, 90)( 52, 89)( 53, 93)( 54, 97)( 55, 96)( 56, 95)( 57, 94)( 58, 98)
( 59,102)( 60,101)( 61,100)( 62, 99)( 63,108)( 64,112)( 65,111)( 66,110)
( 67,109)( 68,103)( 69,107)( 70,106)( 71,105)( 72,104)( 73,118)( 74,122)
( 75,121)( 76,120)( 77,119)( 78,113)( 79,117)( 80,116)( 81,115)( 82,114)
(163,283)(164,287)(165,286)(166,285)(167,284)(168,288)(169,292)(170,291)
(171,290)(172,289)(173,293)(174,297)(175,296)(176,295)(177,294)(178,298)
(179,302)(180,301)(181,300)(182,299)(183,308)(184,312)(185,311)(186,310)
(187,309)(188,303)(189,307)(190,306)(191,305)(192,304)(193,318)(194,322)
(195,321)(196,320)(197,319)(198,313)(199,317)(200,316)(201,315)(202,314)
(203,243)(204,247)(205,246)(206,245)(207,244)(208,248)(209,252)(210,251)
(211,250)(212,249)(213,253)(214,257)(215,256)(216,255)(217,254)(218,258)
(219,262)(220,261)(221,260)(222,259)(223,268)(224,272)(225,271)(226,270)
(227,269)(228,263)(229,267)(230,266)(231,265)(232,264)(233,278)(234,282)
(235,281)(236,280)(237,279)(238,273)(239,277)(240,276)(241,275)(242,274);;
s4 := ( 3, 44)( 4, 43)( 5, 47)( 6, 46)( 7, 45)( 8, 49)( 9, 48)( 10, 52)
( 11, 51)( 12, 50)( 13, 54)( 14, 53)( 15, 57)( 16, 56)( 17, 55)( 18, 59)
( 19, 58)( 20, 62)( 21, 61)( 22, 60)( 23, 64)( 24, 63)( 25, 67)( 26, 66)
( 27, 65)( 28, 69)( 29, 68)( 30, 72)( 31, 71)( 32, 70)( 33, 74)( 34, 73)
( 35, 77)( 36, 76)( 37, 75)( 38, 79)( 39, 78)( 40, 82)( 41, 81)( 42, 80)
( 83,124)( 84,123)( 85,127)( 86,126)( 87,125)( 88,129)( 89,128)( 90,132)
( 91,131)( 92,130)( 93,134)( 94,133)( 95,137)( 96,136)( 97,135)( 98,139)
( 99,138)(100,142)(101,141)(102,140)(103,144)(104,143)(105,147)(106,146)
(107,145)(108,149)(109,148)(110,152)(111,151)(112,150)(113,154)(114,153)
(115,157)(116,156)(117,155)(118,159)(119,158)(120,162)(121,161)(122,160)
(163,204)(164,203)(165,207)(166,206)(167,205)(168,209)(169,208)(170,212)
(171,211)(172,210)(173,214)(174,213)(175,217)(176,216)(177,215)(178,219)
(179,218)(180,222)(181,221)(182,220)(183,224)(184,223)(185,227)(186,226)
(187,225)(188,229)(189,228)(190,232)(191,231)(192,230)(193,234)(194,233)
(195,237)(196,236)(197,235)(198,239)(199,238)(200,242)(201,241)(202,240)
(243,284)(244,283)(245,287)(246,286)(247,285)(248,289)(249,288)(250,292)
(251,291)(252,290)(253,294)(254,293)(255,297)(256,296)(257,295)(258,299)
(259,298)(260,302)(261,301)(262,300)(263,304)(264,303)(265,307)(266,306)
(267,305)(268,309)(269,308)(270,312)(271,311)(272,310)(273,314)(274,313)
(275,317)(276,316)(277,315)(278,319)(279,318)(280,322)(281,321)(282,320);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!(1,2);
s1 := Sym(322)!( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)( 8,168)( 9,169)
( 10,170)( 11,171)( 12,172)( 13,178)( 14,179)( 15,180)( 16,181)( 17,182)
( 18,173)( 19,174)( 20,175)( 21,176)( 22,177)( 23,188)( 24,189)( 25,190)
( 26,191)( 27,192)( 28,183)( 29,184)( 30,185)( 31,186)( 32,187)( 33,193)
( 34,194)( 35,195)( 36,196)( 37,197)( 38,198)( 39,199)( 40,200)( 41,201)
( 42,202)( 43,203)( 44,204)( 45,205)( 46,206)( 47,207)( 48,208)( 49,209)
( 50,210)( 51,211)( 52,212)( 53,218)( 54,219)( 55,220)( 56,221)( 57,222)
( 58,213)( 59,214)( 60,215)( 61,216)( 62,217)( 63,228)( 64,229)( 65,230)
( 66,231)( 67,232)( 68,223)( 69,224)( 70,225)( 71,226)( 72,227)( 73,233)
( 74,234)( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)( 80,240)( 81,241)
( 82,242)( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)( 88,248)( 89,249)
( 90,250)( 91,251)( 92,252)( 93,258)( 94,259)( 95,260)( 96,261)( 97,262)
( 98,253)( 99,254)(100,255)(101,256)(102,257)(103,268)(104,269)(105,270)
(106,271)(107,272)(108,263)(109,264)(110,265)(111,266)(112,267)(113,273)
(114,274)(115,275)(116,276)(117,277)(118,278)(119,279)(120,280)(121,281)
(122,282)(123,283)(124,284)(125,285)(126,286)(127,287)(128,288)(129,289)
(130,290)(131,291)(132,292)(133,298)(134,299)(135,300)(136,301)(137,302)
(138,293)(139,294)(140,295)(141,296)(142,297)(143,308)(144,309)(145,310)
(146,311)(147,312)(148,303)(149,304)(150,305)(151,306)(152,307)(153,313)
(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)(160,320)(161,321)
(162,322);
s2 := Sym(322)!( 23, 28)( 24, 29)( 25, 30)( 26, 31)( 27, 32)( 33, 38)( 34, 39)
( 35, 40)( 36, 41)( 37, 42)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)
( 73, 78)( 74, 79)( 75, 80)( 76, 81)( 77, 82)( 83, 93)( 84, 94)( 85, 95)
( 86, 96)( 87, 97)( 88, 98)( 89, 99)( 90,100)( 91,101)( 92,102)(103,118)
(104,119)(105,120)(106,121)(107,122)(108,113)(109,114)(110,115)(111,116)
(112,117)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)
(130,140)(131,141)(132,142)(143,158)(144,159)(145,160)(146,161)(147,162)
(148,153)(149,154)(150,155)(151,156)(152,157)(163,183)(164,184)(165,185)
(166,186)(167,187)(168,188)(169,189)(170,190)(171,191)(172,192)(173,193)
(174,194)(175,195)(176,196)(177,197)(178,198)(179,199)(180,200)(181,201)
(182,202)(203,223)(204,224)(205,225)(206,226)(207,227)(208,228)(209,229)
(210,230)(211,231)(212,232)(213,233)(214,234)(215,235)(216,236)(217,237)
(218,238)(219,239)(220,240)(221,241)(222,242)(243,278)(244,279)(245,280)
(246,281)(247,282)(248,273)(249,274)(250,275)(251,276)(252,277)(253,268)
(254,269)(255,270)(256,271)(257,272)(258,263)(259,264)(260,265)(261,266)
(262,267)(283,318)(284,319)(285,320)(286,321)(287,322)(288,313)(289,314)
(290,315)(291,316)(292,317)(293,308)(294,309)(295,310)(296,311)(297,312)
(298,303)(299,304)(300,305)(301,306)(302,307);
s3 := Sym(322)!( 3,123)( 4,127)( 5,126)( 6,125)( 7,124)( 8,128)( 9,132)
( 10,131)( 11,130)( 12,129)( 13,133)( 14,137)( 15,136)( 16,135)( 17,134)
( 18,138)( 19,142)( 20,141)( 21,140)( 22,139)( 23,148)( 24,152)( 25,151)
( 26,150)( 27,149)( 28,143)( 29,147)( 30,146)( 31,145)( 32,144)( 33,158)
( 34,162)( 35,161)( 36,160)( 37,159)( 38,153)( 39,157)( 40,156)( 41,155)
( 42,154)( 43, 83)( 44, 87)( 45, 86)( 46, 85)( 47, 84)( 48, 88)( 49, 92)
( 50, 91)( 51, 90)( 52, 89)( 53, 93)( 54, 97)( 55, 96)( 56, 95)( 57, 94)
( 58, 98)( 59,102)( 60,101)( 61,100)( 62, 99)( 63,108)( 64,112)( 65,111)
( 66,110)( 67,109)( 68,103)( 69,107)( 70,106)( 71,105)( 72,104)( 73,118)
( 74,122)( 75,121)( 76,120)( 77,119)( 78,113)( 79,117)( 80,116)( 81,115)
( 82,114)(163,283)(164,287)(165,286)(166,285)(167,284)(168,288)(169,292)
(170,291)(171,290)(172,289)(173,293)(174,297)(175,296)(176,295)(177,294)
(178,298)(179,302)(180,301)(181,300)(182,299)(183,308)(184,312)(185,311)
(186,310)(187,309)(188,303)(189,307)(190,306)(191,305)(192,304)(193,318)
(194,322)(195,321)(196,320)(197,319)(198,313)(199,317)(200,316)(201,315)
(202,314)(203,243)(204,247)(205,246)(206,245)(207,244)(208,248)(209,252)
(210,251)(211,250)(212,249)(213,253)(214,257)(215,256)(216,255)(217,254)
(218,258)(219,262)(220,261)(221,260)(222,259)(223,268)(224,272)(225,271)
(226,270)(227,269)(228,263)(229,267)(230,266)(231,265)(232,264)(233,278)
(234,282)(235,281)(236,280)(237,279)(238,273)(239,277)(240,276)(241,275)
(242,274);
s4 := Sym(322)!( 3, 44)( 4, 43)( 5, 47)( 6, 46)( 7, 45)( 8, 49)( 9, 48)
( 10, 52)( 11, 51)( 12, 50)( 13, 54)( 14, 53)( 15, 57)( 16, 56)( 17, 55)
( 18, 59)( 19, 58)( 20, 62)( 21, 61)( 22, 60)( 23, 64)( 24, 63)( 25, 67)
( 26, 66)( 27, 65)( 28, 69)( 29, 68)( 30, 72)( 31, 71)( 32, 70)( 33, 74)
( 34, 73)( 35, 77)( 36, 76)( 37, 75)( 38, 79)( 39, 78)( 40, 82)( 41, 81)
( 42, 80)( 83,124)( 84,123)( 85,127)( 86,126)( 87,125)( 88,129)( 89,128)
( 90,132)( 91,131)( 92,130)( 93,134)( 94,133)( 95,137)( 96,136)( 97,135)
( 98,139)( 99,138)(100,142)(101,141)(102,140)(103,144)(104,143)(105,147)
(106,146)(107,145)(108,149)(109,148)(110,152)(111,151)(112,150)(113,154)
(114,153)(115,157)(116,156)(117,155)(118,159)(119,158)(120,162)(121,161)
(122,160)(163,204)(164,203)(165,207)(166,206)(167,205)(168,209)(169,208)
(170,212)(171,211)(172,210)(173,214)(174,213)(175,217)(176,216)(177,215)
(178,219)(179,218)(180,222)(181,221)(182,220)(183,224)(184,223)(185,227)
(186,226)(187,225)(188,229)(189,228)(190,232)(191,231)(192,230)(193,234)
(194,233)(195,237)(196,236)(197,235)(198,239)(199,238)(200,242)(201,241)
(202,240)(243,284)(244,283)(245,287)(246,286)(247,285)(248,289)(249,288)
(250,292)(251,291)(252,290)(253,294)(254,293)(255,297)(256,296)(257,295)
(258,299)(259,298)(260,302)(261,301)(262,300)(263,304)(264,303)(265,307)
(266,306)(267,305)(268,309)(269,308)(270,312)(271,311)(272,310)(273,314)
(274,313)(275,317)(276,316)(277,315)(278,319)(279,318)(280,322)(281,321)
(282,320);
poly := sub<Sym(322)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope