Polytope of Type {330}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {330}*660
Also Known As : 330-gon, {330}. if this polytope has another name.
Group : SmallGroup(660,39)
Rank : 2
Schlafli Type : {330}
Number of vertices, edges, etc : 330, 330
Order of s0s1 : 330
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{330,2} of size 1320
Vertex Figure Of :
{2,330} of size 1320
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {165}*330
3-fold quotients : {110}*220
5-fold quotients : {66}*132
6-fold quotients : {55}*110
10-fold quotients : {33}*66
11-fold quotients : {30}*60
15-fold quotients : {22}*44
22-fold quotients : {15}*30
30-fold quotients : {11}*22
33-fold quotients : {10}*20
55-fold quotients : {6}*12
66-fold quotients : {5}*10
110-fold quotients : {3}*6
165-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {660}*1320
3-fold covers : {990}*1980
Permutation Representation (GAP) :
s0 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 12, 45)( 13, 55)( 14, 54)
( 15, 53)( 16, 52)( 17, 51)( 18, 50)( 19, 49)( 20, 48)( 21, 47)( 22, 46)
( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)( 29, 39)( 30, 38)
( 31, 37)( 32, 36)( 33, 35)( 56,111)( 57,121)( 58,120)( 59,119)( 60,118)
( 61,117)( 62,116)( 63,115)( 64,114)( 65,113)( 66,112)( 67,155)( 68,165)
( 69,164)( 70,163)( 71,162)( 72,161)( 73,160)( 74,159)( 75,158)( 76,157)
( 77,156)( 78,144)( 79,154)( 80,153)( 81,152)( 82,151)( 83,150)( 84,149)
( 85,148)( 86,147)( 87,146)( 88,145)( 89,133)( 90,143)( 91,142)( 92,141)
( 93,140)( 94,139)( 95,138)( 96,137)( 97,136)( 98,135)( 99,134)(100,122)
(101,132)(102,131)(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)
(109,124)(110,123)(167,176)(168,175)(169,174)(170,173)(171,172)(177,210)
(178,220)(179,219)(180,218)(181,217)(182,216)(183,215)(184,214)(185,213)
(186,212)(187,211)(188,199)(189,209)(190,208)(191,207)(192,206)(193,205)
(194,204)(195,203)(196,202)(197,201)(198,200)(221,276)(222,286)(223,285)
(224,284)(225,283)(226,282)(227,281)(228,280)(229,279)(230,278)(231,277)
(232,320)(233,330)(234,329)(235,328)(236,327)(237,326)(238,325)(239,324)
(240,323)(241,322)(242,321)(243,309)(244,319)(245,318)(246,317)(247,316)
(248,315)(249,314)(250,313)(251,312)(252,311)(253,310)(254,298)(255,308)
(256,307)(257,306)(258,305)(259,304)(260,303)(261,302)(262,301)(263,300)
(264,299)(265,287)(266,297)(267,296)(268,295)(269,294)(270,293)(271,292)
(272,291)(273,290)(274,289)(275,288);;
s1 := ( 1,233)( 2,232)( 3,242)( 4,241)( 5,240)( 6,239)( 7,238)( 8,237)
( 9,236)( 10,235)( 11,234)( 12,222)( 13,221)( 14,231)( 15,230)( 16,229)
( 17,228)( 18,227)( 19,226)( 20,225)( 21,224)( 22,223)( 23,266)( 24,265)
( 25,275)( 26,274)( 27,273)( 28,272)( 29,271)( 30,270)( 31,269)( 32,268)
( 33,267)( 34,255)( 35,254)( 36,264)( 37,263)( 38,262)( 39,261)( 40,260)
( 41,259)( 42,258)( 43,257)( 44,256)( 45,244)( 46,243)( 47,253)( 48,252)
( 49,251)( 50,250)( 51,249)( 52,248)( 53,247)( 54,246)( 55,245)( 56,178)
( 57,177)( 58,187)( 59,186)( 60,185)( 61,184)( 62,183)( 63,182)( 64,181)
( 65,180)( 66,179)( 67,167)( 68,166)( 69,176)( 70,175)( 71,174)( 72,173)
( 73,172)( 74,171)( 75,170)( 76,169)( 77,168)( 78,211)( 79,210)( 80,220)
( 81,219)( 82,218)( 83,217)( 84,216)( 85,215)( 86,214)( 87,213)( 88,212)
( 89,200)( 90,199)( 91,209)( 92,208)( 93,207)( 94,206)( 95,205)( 96,204)
( 97,203)( 98,202)( 99,201)(100,189)(101,188)(102,198)(103,197)(104,196)
(105,195)(106,194)(107,193)(108,192)(109,191)(110,190)(111,288)(112,287)
(113,297)(114,296)(115,295)(116,294)(117,293)(118,292)(119,291)(120,290)
(121,289)(122,277)(123,276)(124,286)(125,285)(126,284)(127,283)(128,282)
(129,281)(130,280)(131,279)(132,278)(133,321)(134,320)(135,330)(136,329)
(137,328)(138,327)(139,326)(140,325)(141,324)(142,323)(143,322)(144,310)
(145,309)(146,319)(147,318)(148,317)(149,316)(150,315)(151,314)(152,313)
(153,312)(154,311)(155,299)(156,298)(157,308)(158,307)(159,306)(160,305)
(161,304)(162,303)(163,302)(164,301)(165,300);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*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*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*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*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(330)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 12, 45)( 13, 55)
( 14, 54)( 15, 53)( 16, 52)( 17, 51)( 18, 50)( 19, 49)( 20, 48)( 21, 47)
( 22, 46)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)( 29, 39)
( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 56,111)( 57,121)( 58,120)( 59,119)
( 60,118)( 61,117)( 62,116)( 63,115)( 64,114)( 65,113)( 66,112)( 67,155)
( 68,165)( 69,164)( 70,163)( 71,162)( 72,161)( 73,160)( 74,159)( 75,158)
( 76,157)( 77,156)( 78,144)( 79,154)( 80,153)( 81,152)( 82,151)( 83,150)
( 84,149)( 85,148)( 86,147)( 87,146)( 88,145)( 89,133)( 90,143)( 91,142)
( 92,141)( 93,140)( 94,139)( 95,138)( 96,137)( 97,136)( 98,135)( 99,134)
(100,122)(101,132)(102,131)(103,130)(104,129)(105,128)(106,127)(107,126)
(108,125)(109,124)(110,123)(167,176)(168,175)(169,174)(170,173)(171,172)
(177,210)(178,220)(179,219)(180,218)(181,217)(182,216)(183,215)(184,214)
(185,213)(186,212)(187,211)(188,199)(189,209)(190,208)(191,207)(192,206)
(193,205)(194,204)(195,203)(196,202)(197,201)(198,200)(221,276)(222,286)
(223,285)(224,284)(225,283)(226,282)(227,281)(228,280)(229,279)(230,278)
(231,277)(232,320)(233,330)(234,329)(235,328)(236,327)(237,326)(238,325)
(239,324)(240,323)(241,322)(242,321)(243,309)(244,319)(245,318)(246,317)
(247,316)(248,315)(249,314)(250,313)(251,312)(252,311)(253,310)(254,298)
(255,308)(256,307)(257,306)(258,305)(259,304)(260,303)(261,302)(262,301)
(263,300)(264,299)(265,287)(266,297)(267,296)(268,295)(269,294)(270,293)
(271,292)(272,291)(273,290)(274,289)(275,288);
s1 := Sym(330)!( 1,233)( 2,232)( 3,242)( 4,241)( 5,240)( 6,239)( 7,238)
( 8,237)( 9,236)( 10,235)( 11,234)( 12,222)( 13,221)( 14,231)( 15,230)
( 16,229)( 17,228)( 18,227)( 19,226)( 20,225)( 21,224)( 22,223)( 23,266)
( 24,265)( 25,275)( 26,274)( 27,273)( 28,272)( 29,271)( 30,270)( 31,269)
( 32,268)( 33,267)( 34,255)( 35,254)( 36,264)( 37,263)( 38,262)( 39,261)
( 40,260)( 41,259)( 42,258)( 43,257)( 44,256)( 45,244)( 46,243)( 47,253)
( 48,252)( 49,251)( 50,250)( 51,249)( 52,248)( 53,247)( 54,246)( 55,245)
( 56,178)( 57,177)( 58,187)( 59,186)( 60,185)( 61,184)( 62,183)( 63,182)
( 64,181)( 65,180)( 66,179)( 67,167)( 68,166)( 69,176)( 70,175)( 71,174)
( 72,173)( 73,172)( 74,171)( 75,170)( 76,169)( 77,168)( 78,211)( 79,210)
( 80,220)( 81,219)( 82,218)( 83,217)( 84,216)( 85,215)( 86,214)( 87,213)
( 88,212)( 89,200)( 90,199)( 91,209)( 92,208)( 93,207)( 94,206)( 95,205)
( 96,204)( 97,203)( 98,202)( 99,201)(100,189)(101,188)(102,198)(103,197)
(104,196)(105,195)(106,194)(107,193)(108,192)(109,191)(110,190)(111,288)
(112,287)(113,297)(114,296)(115,295)(116,294)(117,293)(118,292)(119,291)
(120,290)(121,289)(122,277)(123,276)(124,286)(125,285)(126,284)(127,283)
(128,282)(129,281)(130,280)(131,279)(132,278)(133,321)(134,320)(135,330)
(136,329)(137,328)(138,327)(139,326)(140,325)(141,324)(142,323)(143,322)
(144,310)(145,309)(146,319)(147,318)(148,317)(149,316)(150,315)(151,314)
(152,313)(153,312)(154,311)(155,299)(156,298)(157,308)(158,307)(159,306)
(160,305)(161,304)(162,303)(163,302)(164,301)(165,300);
poly := sub<Sym(330)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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