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