Polytope of Type {30,22}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,22}*1320
Also Known As : {30,22|2}. if this polytope has another name.
Group : SmallGroup(1320,168)
Rank : 3
Schlafli Type : {30,22}
Number of vertices, edges, etc : 30, 330, 22
Order of s0s1s2 : 330
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) :
3-fold quotients : {10,22}*440
5-fold quotients : {6,22}*264
11-fold quotients : {30,2}*120
15-fold quotients : {2,22}*88
22-fold quotients : {15,2}*60
30-fold quotients : {2,11}*44
33-fold quotients : {10,2}*40
55-fold quotients : {6,2}*24
66-fold quotients : {5,2}*20
110-fold quotients : {3,2}*12
165-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 12, 45)( 13, 46)( 14, 47)( 15, 48)( 16, 49)( 17, 50)( 18, 51)( 19, 52)
( 20, 53)( 21, 54)( 22, 55)( 23, 34)( 24, 35)( 25, 36)( 26, 37)( 27, 38)
( 28, 39)( 29, 40)( 30, 41)( 31, 42)( 32, 43)( 33, 44)( 56,111)( 57,112)
( 58,113)( 59,114)( 60,115)( 61,116)( 62,117)( 63,118)( 64,119)( 65,120)
( 66,121)( 67,155)( 68,156)( 69,157)( 70,158)( 71,159)( 72,160)( 73,161)
( 74,162)( 75,163)( 76,164)( 77,165)( 78,144)( 79,145)( 80,146)( 81,147)
( 82,148)( 83,149)( 84,150)( 85,151)( 86,152)( 87,153)( 88,154)( 89,133)
( 90,134)( 91,135)( 92,136)( 93,137)( 94,138)( 95,139)( 96,140)( 97,141)
( 98,142)( 99,143)(100,122)(101,123)(102,124)(103,125)(104,126)(105,127)
(106,128)(107,129)(108,130)(109,131)(110,132)(177,210)(178,211)(179,212)
(180,213)(181,214)(182,215)(183,216)(184,217)(185,218)(186,219)(187,220)
(188,199)(189,200)(190,201)(191,202)(192,203)(193,204)(194,205)(195,206)
(196,207)(197,208)(198,209)(221,276)(222,277)(223,278)(224,279)(225,280)
(226,281)(227,282)(228,283)(229,284)(230,285)(231,286)(232,320)(233,321)
(234,322)(235,323)(236,324)(237,325)(238,326)(239,327)(240,328)(241,329)
(242,330)(243,309)(244,310)(245,311)(246,312)(247,313)(248,314)(249,315)
(250,316)(251,317)(252,318)(253,319)(254,298)(255,299)(256,300)(257,301)
(258,302)(259,303)(260,304)(261,305)(262,306)(263,307)(264,308)(265,287)
(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)(272,294)(273,295)
(274,296)(275,297);;
s1 := ( 1, 67)( 2, 77)( 3, 76)( 4, 75)( 5, 74)( 6, 73)( 7, 72)( 8, 71)
( 9, 70)( 10, 69)( 11, 68)( 12, 56)( 13, 66)( 14, 65)( 15, 64)( 16, 63)
( 17, 62)( 18, 61)( 19, 60)( 20, 59)( 21, 58)( 22, 57)( 23,100)( 24,110)
( 25,109)( 26,108)( 27,107)( 28,106)( 29,105)( 30,104)( 31,103)( 32,102)
( 33,101)( 34, 89)( 35, 99)( 36, 98)( 37, 97)( 38, 96)( 39, 95)( 40, 94)
( 41, 93)( 42, 92)( 43, 91)( 44, 90)( 45, 78)( 46, 88)( 47, 87)( 48, 86)
( 49, 85)( 50, 84)( 51, 83)( 52, 82)( 53, 81)( 54, 80)( 55, 79)(111,122)
(112,132)(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)
(120,124)(121,123)(133,155)(134,165)(135,164)(136,163)(137,162)(138,161)
(139,160)(140,159)(141,158)(142,157)(143,156)(145,154)(146,153)(147,152)
(148,151)(149,150)(166,232)(167,242)(168,241)(169,240)(170,239)(171,238)
(172,237)(173,236)(174,235)(175,234)(176,233)(177,221)(178,231)(179,230)
(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)(186,223)(187,222)
(188,265)(189,275)(190,274)(191,273)(192,272)(193,271)(194,270)(195,269)
(196,268)(197,267)(198,266)(199,254)(200,264)(201,263)(202,262)(203,261)
(204,260)(205,259)(206,258)(207,257)(208,256)(209,255)(210,243)(211,253)
(212,252)(213,251)(214,250)(215,249)(216,248)(217,247)(218,246)(219,245)
(220,244)(276,287)(277,297)(278,296)(279,295)(280,294)(281,293)(282,292)
(283,291)(284,290)(285,289)(286,288)(298,320)(299,330)(300,329)(301,328)
(302,327)(303,326)(304,325)(305,324)(306,323)(307,322)(308,321)(310,319)
(311,318)(312,317)(313,316)(314,315);;
s2 := ( 1,167)( 2,166)( 3,176)( 4,175)( 5,174)( 6,173)( 7,172)( 8,171)
( 9,170)( 10,169)( 11,168)( 12,178)( 13,177)( 14,187)( 15,186)( 16,185)
( 17,184)( 18,183)( 19,182)( 20,181)( 21,180)( 22,179)( 23,189)( 24,188)
( 25,198)( 26,197)( 27,196)( 28,195)( 29,194)( 30,193)( 31,192)( 32,191)
( 33,190)( 34,200)( 35,199)( 36,209)( 37,208)( 38,207)( 39,206)( 40,205)
( 41,204)( 42,203)( 43,202)( 44,201)( 45,211)( 46,210)( 47,220)( 48,219)
( 49,218)( 50,217)( 51,216)( 52,215)( 53,214)( 54,213)( 55,212)( 56,222)
( 57,221)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)( 64,225)
( 65,224)( 66,223)( 67,233)( 68,232)( 69,242)( 70,241)( 71,240)( 72,239)
( 73,238)( 74,237)( 75,236)( 76,235)( 77,234)( 78,244)( 79,243)( 80,253)
( 81,252)( 82,251)( 83,250)( 84,249)( 85,248)( 86,247)( 87,246)( 88,245)
( 89,255)( 90,254)( 91,264)( 92,263)( 93,262)( 94,261)( 95,260)( 96,259)
( 97,258)( 98,257)( 99,256)(100,266)(101,265)(102,275)(103,274)(104,273)
(105,272)(106,271)(107,270)(108,269)(109,268)(110,267)(111,277)(112,276)
(113,286)(114,285)(115,284)(116,283)(117,282)(118,281)(119,280)(120,279)
(121,278)(122,288)(123,287)(124,297)(125,296)(126,295)(127,294)(128,293)
(129,292)(130,291)(131,290)(132,289)(133,299)(134,298)(135,308)(136,307)
(137,306)(138,305)(139,304)(140,303)(141,302)(142,301)(143,300)(144,310)
(145,309)(146,319)(147,318)(148,317)(149,316)(150,315)(151,314)(152,313)
(153,312)(154,311)(155,321)(156,320)(157,330)(158,329)(159,328)(160,327)
(161,326)(162,325)(163,324)(164,323)(165,322);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(330)!( 12, 45)( 13, 46)( 14, 47)( 15, 48)( 16, 49)( 17, 50)( 18, 51)
( 19, 52)( 20, 53)( 21, 54)( 22, 55)( 23, 34)( 24, 35)( 25, 36)( 26, 37)
( 27, 38)( 28, 39)( 29, 40)( 30, 41)( 31, 42)( 32, 43)( 33, 44)( 56,111)
( 57,112)( 58,113)( 59,114)( 60,115)( 61,116)( 62,117)( 63,118)( 64,119)
( 65,120)( 66,121)( 67,155)( 68,156)( 69,157)( 70,158)( 71,159)( 72,160)
( 73,161)( 74,162)( 75,163)( 76,164)( 77,165)( 78,144)( 79,145)( 80,146)
( 81,147)( 82,148)( 83,149)( 84,150)( 85,151)( 86,152)( 87,153)( 88,154)
( 89,133)( 90,134)( 91,135)( 92,136)( 93,137)( 94,138)( 95,139)( 96,140)
( 97,141)( 98,142)( 99,143)(100,122)(101,123)(102,124)(103,125)(104,126)
(105,127)(106,128)(107,129)(108,130)(109,131)(110,132)(177,210)(178,211)
(179,212)(180,213)(181,214)(182,215)(183,216)(184,217)(185,218)(186,219)
(187,220)(188,199)(189,200)(190,201)(191,202)(192,203)(193,204)(194,205)
(195,206)(196,207)(197,208)(198,209)(221,276)(222,277)(223,278)(224,279)
(225,280)(226,281)(227,282)(228,283)(229,284)(230,285)(231,286)(232,320)
(233,321)(234,322)(235,323)(236,324)(237,325)(238,326)(239,327)(240,328)
(241,329)(242,330)(243,309)(244,310)(245,311)(246,312)(247,313)(248,314)
(249,315)(250,316)(251,317)(252,318)(253,319)(254,298)(255,299)(256,300)
(257,301)(258,302)(259,303)(260,304)(261,305)(262,306)(263,307)(264,308)
(265,287)(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)(272,294)
(273,295)(274,296)(275,297);
s1 := Sym(330)!( 1, 67)( 2, 77)( 3, 76)( 4, 75)( 5, 74)( 6, 73)( 7, 72)
( 8, 71)( 9, 70)( 10, 69)( 11, 68)( 12, 56)( 13, 66)( 14, 65)( 15, 64)
( 16, 63)( 17, 62)( 18, 61)( 19, 60)( 20, 59)( 21, 58)( 22, 57)( 23,100)
( 24,110)( 25,109)( 26,108)( 27,107)( 28,106)( 29,105)( 30,104)( 31,103)
( 32,102)( 33,101)( 34, 89)( 35, 99)( 36, 98)( 37, 97)( 38, 96)( 39, 95)
( 40, 94)( 41, 93)( 42, 92)( 43, 91)( 44, 90)( 45, 78)( 46, 88)( 47, 87)
( 48, 86)( 49, 85)( 50, 84)( 51, 83)( 52, 82)( 53, 81)( 54, 80)( 55, 79)
(111,122)(112,132)(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)
(119,125)(120,124)(121,123)(133,155)(134,165)(135,164)(136,163)(137,162)
(138,161)(139,160)(140,159)(141,158)(142,157)(143,156)(145,154)(146,153)
(147,152)(148,151)(149,150)(166,232)(167,242)(168,241)(169,240)(170,239)
(171,238)(172,237)(173,236)(174,235)(175,234)(176,233)(177,221)(178,231)
(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)(186,223)
(187,222)(188,265)(189,275)(190,274)(191,273)(192,272)(193,271)(194,270)
(195,269)(196,268)(197,267)(198,266)(199,254)(200,264)(201,263)(202,262)
(203,261)(204,260)(205,259)(206,258)(207,257)(208,256)(209,255)(210,243)
(211,253)(212,252)(213,251)(214,250)(215,249)(216,248)(217,247)(218,246)
(219,245)(220,244)(276,287)(277,297)(278,296)(279,295)(280,294)(281,293)
(282,292)(283,291)(284,290)(285,289)(286,288)(298,320)(299,330)(300,329)
(301,328)(302,327)(303,326)(304,325)(305,324)(306,323)(307,322)(308,321)
(310,319)(311,318)(312,317)(313,316)(314,315);
s2 := Sym(330)!( 1,167)( 2,166)( 3,176)( 4,175)( 5,174)( 6,173)( 7,172)
( 8,171)( 9,170)( 10,169)( 11,168)( 12,178)( 13,177)( 14,187)( 15,186)
( 16,185)( 17,184)( 18,183)( 19,182)( 20,181)( 21,180)( 22,179)( 23,189)
( 24,188)( 25,198)( 26,197)( 27,196)( 28,195)( 29,194)( 30,193)( 31,192)
( 32,191)( 33,190)( 34,200)( 35,199)( 36,209)( 37,208)( 38,207)( 39,206)
( 40,205)( 41,204)( 42,203)( 43,202)( 44,201)( 45,211)( 46,210)( 47,220)
( 48,219)( 49,218)( 50,217)( 51,216)( 52,215)( 53,214)( 54,213)( 55,212)
( 56,222)( 57,221)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)
( 64,225)( 65,224)( 66,223)( 67,233)( 68,232)( 69,242)( 70,241)( 71,240)
( 72,239)( 73,238)( 74,237)( 75,236)( 76,235)( 77,234)( 78,244)( 79,243)
( 80,253)( 81,252)( 82,251)( 83,250)( 84,249)( 85,248)( 86,247)( 87,246)
( 88,245)( 89,255)( 90,254)( 91,264)( 92,263)( 93,262)( 94,261)( 95,260)
( 96,259)( 97,258)( 98,257)( 99,256)(100,266)(101,265)(102,275)(103,274)
(104,273)(105,272)(106,271)(107,270)(108,269)(109,268)(110,267)(111,277)
(112,276)(113,286)(114,285)(115,284)(116,283)(117,282)(118,281)(119,280)
(120,279)(121,278)(122,288)(123,287)(124,297)(125,296)(126,295)(127,294)
(128,293)(129,292)(130,291)(131,290)(132,289)(133,299)(134,298)(135,308)
(136,307)(137,306)(138,305)(139,304)(140,303)(141,302)(142,301)(143,300)
(144,310)(145,309)(146,319)(147,318)(148,317)(149,316)(150,315)(151,314)
(152,313)(153,312)(154,311)(155,321)(156,320)(157,330)(158,329)(159,328)
(160,327)(161,326)(162,325)(163,324)(164,323)(165,322);
poly := sub<Sym(330)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope