Polytope of Type {20,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,16}*640b
if this polytope has a name.
Group : SmallGroup(640,2127)
Rank : 3
Schlafli Type : {20,16}
Number of vertices, edges, etc : 20, 160, 16
Order of s0s1s2 : 80
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{20,16,2} of size 1280
Vertex Figure Of :
{2,20,16} of size 1280
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {20,8}*320a
4-fold quotients : {20,4}*160, {10,8}*160
5-fold quotients : {4,16}*128b
8-fold quotients : {20,2}*80, {10,4}*80
10-fold quotients : {4,8}*64a
16-fold quotients : {10,2}*40
20-fold quotients : {4,4}*32, {2,8}*32
32-fold quotients : {5,2}*20
40-fold quotients : {2,4}*16, {4,2}*16
80-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,16}*1280a, {40,16}*1280e, {40,16}*1280f
3-fold covers : {60,16}*1920b, {20,48}*1920b
Permutation Representation (GAP) :
s0 := ( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)( 8, 89)
( 9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)( 16, 96)
( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)( 24,103)
( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)( 32,115)
( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)
( 41,126)( 42,130)( 43,129)( 44,128)( 45,127)( 46,121)( 47,125)( 48,124)
( 49,123)( 50,122)( 51,136)( 52,140)( 53,139)( 54,138)( 55,137)( 56,131)
( 57,135)( 58,134)( 59,133)( 60,132)( 61,146)( 62,150)( 63,149)( 64,148)
( 65,147)( 66,141)( 67,145)( 68,144)( 69,143)( 70,142)( 71,156)( 72,160)
( 73,159)( 74,158)( 75,157)( 76,151)( 77,155)( 78,154)( 79,153)( 80,152)
(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)(168,249)
(169,248)(170,247)(171,251)(172,255)(173,254)(174,253)(175,252)(176,256)
(177,260)(178,259)(179,258)(180,257)(181,261)(182,265)(183,264)(184,263)
(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,271)(192,275)
(193,274)(194,273)(195,272)(196,276)(197,280)(198,279)(199,278)(200,277)
(201,286)(202,290)(203,289)(204,288)(205,287)(206,281)(207,285)(208,284)
(209,283)(210,282)(211,296)(212,300)(213,299)(214,298)(215,297)(216,291)
(217,295)(218,294)(219,293)(220,292)(221,306)(222,310)(223,309)(224,308)
(225,307)(226,301)(227,305)(228,304)(229,303)(230,302)(231,316)(232,320)
(233,319)(234,318)(235,317)(236,311)(237,315)(238,314)(239,313)(240,312);;
s1 := ( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 17)( 12, 16)( 13, 20)( 14, 19)
( 15, 18)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 37)( 32, 36)( 33, 40)
( 34, 39)( 35, 38)( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)( 46, 57)
( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 61, 72)( 62, 71)( 63, 75)( 64, 74)
( 65, 73)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 81,102)( 82,101)
( 83,105)( 84,104)( 85,103)( 86,107)( 87,106)( 88,110)( 89,109)( 90,108)
( 91,117)( 92,116)( 93,120)( 94,119)( 95,118)( 96,112)( 97,111)( 98,115)
( 99,114)(100,113)(121,152)(122,151)(123,155)(124,154)(125,153)(126,157)
(127,156)(128,160)(129,159)(130,158)(131,142)(132,141)(133,145)(134,144)
(135,143)(136,147)(137,146)(138,150)(139,149)(140,148)(161,202)(162,201)
(163,205)(164,204)(165,203)(166,207)(167,206)(168,210)(169,209)(170,208)
(171,217)(172,216)(173,220)(174,219)(175,218)(176,212)(177,211)(178,215)
(179,214)(180,213)(181,222)(182,221)(183,225)(184,224)(185,223)(186,227)
(187,226)(188,230)(189,229)(190,228)(191,237)(192,236)(193,240)(194,239)
(195,238)(196,232)(197,231)(198,235)(199,234)(200,233)(241,307)(242,306)
(243,310)(244,309)(245,308)(246,302)(247,301)(248,305)(249,304)(250,303)
(251,312)(252,311)(253,315)(254,314)(255,313)(256,317)(257,316)(258,320)
(259,319)(260,318)(261,287)(262,286)(263,290)(264,289)(265,288)(266,282)
(267,281)(268,285)(269,284)(270,283)(271,292)(272,291)(273,295)(274,294)
(275,293)(276,297)(277,296)(278,300)(279,299)(280,298);;
s2 := ( 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)
( 41,211)( 42,212)( 43,213)( 44,214)( 45,215)( 46,216)( 47,217)( 48,218)
( 49,219)( 50,220)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)( 56,206)
( 57,207)( 58,208)( 59,209)( 60,210)( 61,236)( 62,237)( 63,238)( 64,239)
( 65,240)( 66,231)( 67,232)( 68,233)( 69,234)( 70,235)( 71,226)( 72,227)
( 73,228)( 74,229)( 75,230)( 76,221)( 77,222)( 78,223)( 79,224)( 80,225)
( 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)
(121,291)(122,292)(123,293)(124,294)(125,295)(126,296)(127,297)(128,298)
(129,299)(130,300)(131,281)(132,282)(133,283)(134,284)(135,285)(136,286)
(137,287)(138,288)(139,289)(140,290)(141,316)(142,317)(143,318)(144,319)
(145,320)(146,311)(147,312)(148,313)(149,314)(150,315)(151,306)(152,307)
(153,308)(154,309)(155,310)(156,301)(157,302)(158,303)(159,304)(160,305);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*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(320)!( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)
( 8, 89)( 9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)
( 16, 96)( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)
( 24,103)( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)
( 32,115)( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)
( 40,117)( 41,126)( 42,130)( 43,129)( 44,128)( 45,127)( 46,121)( 47,125)
( 48,124)( 49,123)( 50,122)( 51,136)( 52,140)( 53,139)( 54,138)( 55,137)
( 56,131)( 57,135)( 58,134)( 59,133)( 60,132)( 61,146)( 62,150)( 63,149)
( 64,148)( 65,147)( 66,141)( 67,145)( 68,144)( 69,143)( 70,142)( 71,156)
( 72,160)( 73,159)( 74,158)( 75,157)( 76,151)( 77,155)( 78,154)( 79,153)
( 80,152)(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)
(168,249)(169,248)(170,247)(171,251)(172,255)(173,254)(174,253)(175,252)
(176,256)(177,260)(178,259)(179,258)(180,257)(181,261)(182,265)(183,264)
(184,263)(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,271)
(192,275)(193,274)(194,273)(195,272)(196,276)(197,280)(198,279)(199,278)
(200,277)(201,286)(202,290)(203,289)(204,288)(205,287)(206,281)(207,285)
(208,284)(209,283)(210,282)(211,296)(212,300)(213,299)(214,298)(215,297)
(216,291)(217,295)(218,294)(219,293)(220,292)(221,306)(222,310)(223,309)
(224,308)(225,307)(226,301)(227,305)(228,304)(229,303)(230,302)(231,316)
(232,320)(233,319)(234,318)(235,317)(236,311)(237,315)(238,314)(239,313)
(240,312);
s1 := Sym(320)!( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 17)( 12, 16)( 13, 20)
( 14, 19)( 15, 18)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)
( 46, 57)( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 61, 72)( 62, 71)( 63, 75)
( 64, 74)( 65, 73)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 81,102)
( 82,101)( 83,105)( 84,104)( 85,103)( 86,107)( 87,106)( 88,110)( 89,109)
( 90,108)( 91,117)( 92,116)( 93,120)( 94,119)( 95,118)( 96,112)( 97,111)
( 98,115)( 99,114)(100,113)(121,152)(122,151)(123,155)(124,154)(125,153)
(126,157)(127,156)(128,160)(129,159)(130,158)(131,142)(132,141)(133,145)
(134,144)(135,143)(136,147)(137,146)(138,150)(139,149)(140,148)(161,202)
(162,201)(163,205)(164,204)(165,203)(166,207)(167,206)(168,210)(169,209)
(170,208)(171,217)(172,216)(173,220)(174,219)(175,218)(176,212)(177,211)
(178,215)(179,214)(180,213)(181,222)(182,221)(183,225)(184,224)(185,223)
(186,227)(187,226)(188,230)(189,229)(190,228)(191,237)(192,236)(193,240)
(194,239)(195,238)(196,232)(197,231)(198,235)(199,234)(200,233)(241,307)
(242,306)(243,310)(244,309)(245,308)(246,302)(247,301)(248,305)(249,304)
(250,303)(251,312)(252,311)(253,315)(254,314)(255,313)(256,317)(257,316)
(258,320)(259,319)(260,318)(261,287)(262,286)(263,290)(264,289)(265,288)
(266,282)(267,281)(268,285)(269,284)(270,283)(271,292)(272,291)(273,295)
(274,294)(275,293)(276,297)(277,296)(278,300)(279,299)(280,298);
s2 := 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)( 41,211)( 42,212)( 43,213)( 44,214)( 45,215)( 46,216)( 47,217)
( 48,218)( 49,219)( 50,220)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)
( 56,206)( 57,207)( 58,208)( 59,209)( 60,210)( 61,236)( 62,237)( 63,238)
( 64,239)( 65,240)( 66,231)( 67,232)( 68,233)( 69,234)( 70,235)( 71,226)
( 72,227)( 73,228)( 74,229)( 75,230)( 76,221)( 77,222)( 78,223)( 79,224)
( 80,225)( 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)(121,291)(122,292)(123,293)(124,294)(125,295)(126,296)(127,297)
(128,298)(129,299)(130,300)(131,281)(132,282)(133,283)(134,284)(135,285)
(136,286)(137,287)(138,288)(139,289)(140,290)(141,316)(142,317)(143,318)
(144,319)(145,320)(146,311)(147,312)(148,313)(149,314)(150,315)(151,306)
(152,307)(153,308)(154,309)(155,310)(156,301)(157,302)(158,303)(159,304)
(160,305);
poly := sub<Sym(320)|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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*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