Polytope of Type {10,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,8}*640b
if this polytope has a name.
Group : SmallGroup(640,14089)
Rank : 4
Schlafli Type : {10,4,8}
Number of vertices, edges, etc : 10, 20, 16, 8
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,4,8,2} of size 1280
Vertex Figure Of :
{2,10,4,8} of size 1280
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,4,4}*320
4-fold quotients : {10,2,4}*160, {10,4,2}*160
5-fold quotients : {2,4,8}*128b
8-fold quotients : {5,2,4}*80, {10,2,2}*80
10-fold quotients : {2,4,4}*64
16-fold quotients : {5,2,2}*40
20-fold quotients : {2,2,4}*32, {2,4,2}*32
40-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,4,8}*1280a, {10,8,8}*1280c, {10,8,8}*1280d, {20,4,8}*1280b
3-fold covers : {30,4,8}*1920b, {10,12,8}*1920b, {10,4,24}*1920b
Permutation Representation (GAP) :
s0 := ( 1, 41)( 2, 45)( 3, 44)( 4, 43)( 5, 42)( 6, 46)( 7, 50)( 8, 49)
( 9, 48)( 10, 47)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)( 16, 56)
( 17, 60)( 18, 59)( 19, 58)( 20, 57)( 21, 61)( 22, 65)( 23, 64)( 24, 63)
( 25, 62)( 26, 66)( 27, 70)( 28, 69)( 29, 68)( 30, 67)( 31, 71)( 32, 75)
( 33, 74)( 34, 73)( 35, 72)( 36, 76)( 37, 80)( 38, 79)( 39, 78)( 40, 77)
( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)( 88,129)
( 89,128)( 90,127)( 91,131)( 92,135)( 93,134)( 94,133)( 95,132)( 96,136)
( 97,140)( 98,139)( 99,138)(100,137)(101,141)(102,145)(103,144)(104,143)
(105,142)(106,146)(107,150)(108,149)(109,148)(110,147)(111,151)(112,155)
(113,154)(114,153)(115,152)(116,156)(117,160)(118,159)(119,158)(120,157)
(161,201)(162,205)(163,204)(164,203)(165,202)(166,206)(167,210)(168,209)
(169,208)(170,207)(171,211)(172,215)(173,214)(174,213)(175,212)(176,216)
(177,220)(178,219)(179,218)(180,217)(181,221)(182,225)(183,224)(184,223)
(185,222)(186,226)(187,230)(188,229)(189,228)(190,227)(191,231)(192,235)
(193,234)(194,233)(195,232)(196,236)(197,240)(198,239)(199,238)(200,237)
(241,281)(242,285)(243,284)(244,283)(245,282)(246,286)(247,290)(248,289)
(249,288)(250,287)(251,291)(252,295)(253,294)(254,293)(255,292)(256,296)
(257,300)(258,299)(259,298)(260,297)(261,301)(262,305)(263,304)(264,303)
(265,302)(266,306)(267,310)(268,309)(269,308)(270,307)(271,311)(272,315)
(273,314)(274,313)(275,312)(276,316)(277,320)(278,319)(279,318)(280,317);;
s1 := ( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,127)( 7,126)( 8,130)
( 9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,137)
( 17,136)( 18,140)( 19,139)( 20,138)( 21,147)( 22,146)( 23,150)( 24,149)
( 25,148)( 26,142)( 27,141)( 28,145)( 29,144)( 30,143)( 31,157)( 32,156)
( 33,160)( 34,159)( 35,158)( 36,152)( 37,151)( 38,155)( 39,154)( 40,153)
( 41, 82)( 42, 81)( 43, 85)( 44, 84)( 45, 83)( 46, 87)( 47, 86)( 48, 90)
( 49, 89)( 50, 88)( 51, 92)( 52, 91)( 53, 95)( 54, 94)( 55, 93)( 56, 97)
( 57, 96)( 58,100)( 59, 99)( 60, 98)( 61,107)( 62,106)( 63,110)( 64,109)
( 65,108)( 66,102)( 67,101)( 68,105)( 69,104)( 70,103)( 71,117)( 72,116)
( 73,120)( 74,119)( 75,118)( 76,112)( 77,111)( 78,115)( 79,114)( 80,113)
(161,282)(162,281)(163,285)(164,284)(165,283)(166,287)(167,286)(168,290)
(169,289)(170,288)(171,292)(172,291)(173,295)(174,294)(175,293)(176,297)
(177,296)(178,300)(179,299)(180,298)(181,307)(182,306)(183,310)(184,309)
(185,308)(186,302)(187,301)(188,305)(189,304)(190,303)(191,317)(192,316)
(193,320)(194,319)(195,318)(196,312)(197,311)(198,315)(199,314)(200,313)
(201,242)(202,241)(203,245)(204,244)(205,243)(206,247)(207,246)(208,250)
(209,249)(210,248)(211,252)(212,251)(213,255)(214,254)(215,253)(216,257)
(217,256)(218,260)(219,259)(220,258)(221,267)(222,266)(223,270)(224,269)
(225,268)(226,262)(227,261)(228,265)(229,264)(230,263)(231,277)(232,276)
(233,280)(234,279)(235,278)(236,272)(237,271)(238,275)(239,274)(240,273);;
s2 := ( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 36)( 32, 37)( 33, 38)
( 34, 39)( 35, 40)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 71, 76)
( 72, 77)( 73, 78)( 74, 79)( 75, 80)( 81, 91)( 82, 92)( 83, 93)( 84, 94)
( 85, 95)( 86, 96)( 87, 97)( 88, 98)( 89, 99)( 90,100)(101,116)(102,117)
(103,118)(104,119)(105,120)(106,111)(107,112)(108,113)(109,114)(110,115)
(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)
(129,139)(130,140)(141,156)(142,157)(143,158)(144,159)(145,160)(146,151)
(147,152)(148,153)(149,154)(150,155)(161,181)(162,182)(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)
(201,221)(202,222)(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)(241,276)(242,277)(243,278)(244,279)
(245,280)(246,271)(247,272)(248,273)(249,274)(250,275)(251,266)(252,267)
(253,268)(254,269)(255,270)(256,261)(257,262)(258,263)(259,264)(260,265)
(281,316)(282,317)(283,318)(284,319)(285,320)(286,311)(287,312)(288,313)
(289,314)(290,315)(291,306)(292,307)(293,308)(294,309)(295,310)(296,301)
(297,302)(298,303)(299,304)(300,305);;
s3 := ( 1,161)( 2,162)( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)( 8,168)
( 9,169)( 10,170)( 11,176)( 12,177)( 13,178)( 14,179)( 15,180)( 16,171)
( 17,172)( 18,173)( 19,174)( 20,175)( 21,186)( 22,187)( 23,188)( 24,189)
( 25,190)( 26,181)( 27,182)( 28,183)( 29,184)( 30,185)( 31,191)( 32,192)
( 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)( 51,216)( 52,217)( 53,218)( 54,219)( 55,220)( 56,211)
( 57,212)( 58,213)( 59,214)( 60,215)( 61,226)( 62,227)( 63,228)( 64,229)
( 65,230)( 66,221)( 67,222)( 68,223)( 69,224)( 70,225)( 71,231)( 72,232)
( 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)( 91,256)( 92,257)( 93,258)( 94,259)( 95,260)( 96,251)
( 97,252)( 98,253)( 99,254)(100,255)(101,266)(102,267)(103,268)(104,269)
(105,270)(106,261)(107,262)(108,263)(109,264)(110,265)(111,271)(112,272)
(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)(131,296)(132,297)(133,298)(134,299)(135,300)(136,291)
(137,292)(138,293)(139,294)(140,295)(141,306)(142,307)(143,308)(144,309)
(145,310)(146,301)(147,302)(148,303)(149,304)(150,305)(151,311)(152,312)
(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)(160,320);;
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*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
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(320)!( 1, 41)( 2, 45)( 3, 44)( 4, 43)( 5, 42)( 6, 46)( 7, 50)
( 8, 49)( 9, 48)( 10, 47)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)
( 16, 56)( 17, 60)( 18, 59)( 19, 58)( 20, 57)( 21, 61)( 22, 65)( 23, 64)
( 24, 63)( 25, 62)( 26, 66)( 27, 70)( 28, 69)( 29, 68)( 30, 67)( 31, 71)
( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 76)( 37, 80)( 38, 79)( 39, 78)
( 40, 77)( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)
( 88,129)( 89,128)( 90,127)( 91,131)( 92,135)( 93,134)( 94,133)( 95,132)
( 96,136)( 97,140)( 98,139)( 99,138)(100,137)(101,141)(102,145)(103,144)
(104,143)(105,142)(106,146)(107,150)(108,149)(109,148)(110,147)(111,151)
(112,155)(113,154)(114,153)(115,152)(116,156)(117,160)(118,159)(119,158)
(120,157)(161,201)(162,205)(163,204)(164,203)(165,202)(166,206)(167,210)
(168,209)(169,208)(170,207)(171,211)(172,215)(173,214)(174,213)(175,212)
(176,216)(177,220)(178,219)(179,218)(180,217)(181,221)(182,225)(183,224)
(184,223)(185,222)(186,226)(187,230)(188,229)(189,228)(190,227)(191,231)
(192,235)(193,234)(194,233)(195,232)(196,236)(197,240)(198,239)(199,238)
(200,237)(241,281)(242,285)(243,284)(244,283)(245,282)(246,286)(247,290)
(248,289)(249,288)(250,287)(251,291)(252,295)(253,294)(254,293)(255,292)
(256,296)(257,300)(258,299)(259,298)(260,297)(261,301)(262,305)(263,304)
(264,303)(265,302)(266,306)(267,310)(268,309)(269,308)(270,307)(271,311)
(272,315)(273,314)(274,313)(275,312)(276,316)(277,320)(278,319)(279,318)
(280,317);
s1 := Sym(320)!( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,127)( 7,126)
( 8,130)( 9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)
( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,147)( 22,146)( 23,150)
( 24,149)( 25,148)( 26,142)( 27,141)( 28,145)( 29,144)( 30,143)( 31,157)
( 32,156)( 33,160)( 34,159)( 35,158)( 36,152)( 37,151)( 38,155)( 39,154)
( 40,153)( 41, 82)( 42, 81)( 43, 85)( 44, 84)( 45, 83)( 46, 87)( 47, 86)
( 48, 90)( 49, 89)( 50, 88)( 51, 92)( 52, 91)( 53, 95)( 54, 94)( 55, 93)
( 56, 97)( 57, 96)( 58,100)( 59, 99)( 60, 98)( 61,107)( 62,106)( 63,110)
( 64,109)( 65,108)( 66,102)( 67,101)( 68,105)( 69,104)( 70,103)( 71,117)
( 72,116)( 73,120)( 74,119)( 75,118)( 76,112)( 77,111)( 78,115)( 79,114)
( 80,113)(161,282)(162,281)(163,285)(164,284)(165,283)(166,287)(167,286)
(168,290)(169,289)(170,288)(171,292)(172,291)(173,295)(174,294)(175,293)
(176,297)(177,296)(178,300)(179,299)(180,298)(181,307)(182,306)(183,310)
(184,309)(185,308)(186,302)(187,301)(188,305)(189,304)(190,303)(191,317)
(192,316)(193,320)(194,319)(195,318)(196,312)(197,311)(198,315)(199,314)
(200,313)(201,242)(202,241)(203,245)(204,244)(205,243)(206,247)(207,246)
(208,250)(209,249)(210,248)(211,252)(212,251)(213,255)(214,254)(215,253)
(216,257)(217,256)(218,260)(219,259)(220,258)(221,267)(222,266)(223,270)
(224,269)(225,268)(226,262)(227,261)(228,265)(229,264)(230,263)(231,277)
(232,276)(233,280)(234,279)(235,278)(236,272)(237,271)(238,275)(239,274)
(240,273);
s2 := Sym(320)!( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 36)( 32, 37)
( 33, 38)( 34, 39)( 35, 40)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)
( 71, 76)( 72, 77)( 73, 78)( 74, 79)( 75, 80)( 81, 91)( 82, 92)( 83, 93)
( 84, 94)( 85, 95)( 86, 96)( 87, 97)( 88, 98)( 89, 99)( 90,100)(101,116)
(102,117)(103,118)(104,119)(105,120)(106,111)(107,112)(108,113)(109,114)
(110,115)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)
(128,138)(129,139)(130,140)(141,156)(142,157)(143,158)(144,159)(145,160)
(146,151)(147,152)(148,153)(149,154)(150,155)(161,181)(162,182)(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)(201,221)(202,222)(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)(241,276)(242,277)(243,278)
(244,279)(245,280)(246,271)(247,272)(248,273)(249,274)(250,275)(251,266)
(252,267)(253,268)(254,269)(255,270)(256,261)(257,262)(258,263)(259,264)
(260,265)(281,316)(282,317)(283,318)(284,319)(285,320)(286,311)(287,312)
(288,313)(289,314)(290,315)(291,306)(292,307)(293,308)(294,309)(295,310)
(296,301)(297,302)(298,303)(299,304)(300,305);
s3 := Sym(320)!( 1,161)( 2,162)( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)
( 8,168)( 9,169)( 10,170)( 11,176)( 12,177)( 13,178)( 14,179)( 15,180)
( 16,171)( 17,172)( 18,173)( 19,174)( 20,175)( 21,186)( 22,187)( 23,188)
( 24,189)( 25,190)( 26,181)( 27,182)( 28,183)( 29,184)( 30,185)( 31,191)
( 32,192)( 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)( 51,216)( 52,217)( 53,218)( 54,219)( 55,220)
( 56,211)( 57,212)( 58,213)( 59,214)( 60,215)( 61,226)( 62,227)( 63,228)
( 64,229)( 65,230)( 66,221)( 67,222)( 68,223)( 69,224)( 70,225)( 71,231)
( 72,232)( 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)( 91,256)( 92,257)( 93,258)( 94,259)( 95,260)
( 96,251)( 97,252)( 98,253)( 99,254)(100,255)(101,266)(102,267)(103,268)
(104,269)(105,270)(106,261)(107,262)(108,263)(109,264)(110,265)(111,271)
(112,272)(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)(131,296)(132,297)(133,298)(134,299)(135,300)
(136,291)(137,292)(138,293)(139,294)(140,295)(141,306)(142,307)(143,308)
(144,309)(145,310)(146,301)(147,302)(148,303)(149,304)(150,305)(151,311)
(152,312)(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)
(160,320);
poly := sub<Sym(320)|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*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 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