Polytope of Type {22,28}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,28}*1232
Also Known As : {22,28|2}. if this polytope has another name.
Group : SmallGroup(1232,97)
Rank : 3
Schlafli Type : {22,28}
Number of vertices, edges, etc : 22, 308, 28
Order of s0s1s2 : 308
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) :
2-fold quotients : {22,14}*616
7-fold quotients : {22,4}*176
11-fold quotients : {2,28}*112
14-fold quotients : {22,2}*88
22-fold quotients : {2,14}*56
28-fold quotients : {11,2}*44
44-fold quotients : {2,7}*28
77-fold quotients : {2,4}*16
154-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);;
s1 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 68)( 13, 67)( 14, 77)
( 15, 76)( 16, 75)( 17, 74)( 18, 73)( 19, 72)( 20, 71)( 21, 70)( 22, 69)
( 23, 57)( 24, 56)( 25, 66)( 26, 65)( 27, 64)( 28, 63)( 29, 62)( 30, 61)
( 31, 60)( 32, 59)( 33, 58)( 34, 46)( 35, 45)( 36, 55)( 37, 54)( 38, 53)
( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 78, 79)( 80, 88)
( 81, 87)( 82, 86)( 83, 85)( 89,145)( 90,144)( 91,154)( 92,153)( 93,152)
( 94,151)( 95,150)( 96,149)( 97,148)( 98,147)( 99,146)(100,134)(101,133)
(102,143)(103,142)(104,141)(105,140)(106,139)(107,138)(108,137)(109,136)
(110,135)(111,123)(112,122)(113,132)(114,131)(115,130)(116,129)(117,128)
(118,127)(119,126)(120,125)(121,124)(155,233)(156,232)(157,242)(158,241)
(159,240)(160,239)(161,238)(162,237)(163,236)(164,235)(165,234)(166,299)
(167,298)(168,308)(169,307)(170,306)(171,305)(172,304)(173,303)(174,302)
(175,301)(176,300)(177,288)(178,287)(179,297)(180,296)(181,295)(182,294)
(183,293)(184,292)(185,291)(186,290)(187,289)(188,277)(189,276)(190,286)
(191,285)(192,284)(193,283)(194,282)(195,281)(196,280)(197,279)(198,278)
(199,266)(200,265)(201,275)(202,274)(203,273)(204,272)(205,271)(206,270)
(207,269)(208,268)(209,267)(210,255)(211,254)(212,264)(213,263)(214,262)
(215,261)(216,260)(217,259)(218,258)(219,257)(220,256)(221,244)(222,243)
(223,253)(224,252)(225,251)(226,250)(227,249)(228,248)(229,247)(230,246)
(231,245);;
s2 := ( 1,166)( 2,167)( 3,168)( 4,169)( 5,170)( 6,171)( 7,172)( 8,173)
( 9,174)( 10,175)( 11,176)( 12,155)( 13,156)( 14,157)( 15,158)( 16,159)
( 17,160)( 18,161)( 19,162)( 20,163)( 21,164)( 22,165)( 23,221)( 24,222)
( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,229)( 32,230)
( 33,231)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)( 40,216)
( 41,217)( 42,218)( 43,219)( 44,220)( 45,199)( 46,200)( 47,201)( 48,202)
( 49,203)( 50,204)( 51,205)( 52,206)( 53,207)( 54,208)( 55,209)( 56,188)
( 57,189)( 58,190)( 59,191)( 60,192)( 61,193)( 62,194)( 63,195)( 64,196)
( 65,197)( 66,198)( 67,177)( 68,178)( 69,179)( 70,180)( 71,181)( 72,182)
( 73,183)( 74,184)( 75,185)( 76,186)( 77,187)( 78,243)( 79,244)( 80,245)
( 81,246)( 82,247)( 83,248)( 84,249)( 85,250)( 86,251)( 87,252)( 88,253)
( 89,232)( 90,233)( 91,234)( 92,235)( 93,236)( 94,237)( 95,238)( 96,239)
( 97,240)( 98,241)( 99,242)(100,298)(101,299)(102,300)(103,301)(104,302)
(105,303)(106,304)(107,305)(108,306)(109,307)(110,308)(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)(133,265)(134,266)(135,267)(136,268)
(137,269)(138,270)(139,271)(140,272)(141,273)(142,274)(143,275)(144,254)
(145,255)(146,256)(147,257)(148,258)(149,259)(150,260)(151,261)(152,262)
(153,263)(154,264);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(308)!( 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);
s1 := Sym(308)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 68)( 13, 67)
( 14, 77)( 15, 76)( 16, 75)( 17, 74)( 18, 73)( 19, 72)( 20, 71)( 21, 70)
( 22, 69)( 23, 57)( 24, 56)( 25, 66)( 26, 65)( 27, 64)( 28, 63)( 29, 62)
( 30, 61)( 31, 60)( 32, 59)( 33, 58)( 34, 46)( 35, 45)( 36, 55)( 37, 54)
( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 78, 79)
( 80, 88)( 81, 87)( 82, 86)( 83, 85)( 89,145)( 90,144)( 91,154)( 92,153)
( 93,152)( 94,151)( 95,150)( 96,149)( 97,148)( 98,147)( 99,146)(100,134)
(101,133)(102,143)(103,142)(104,141)(105,140)(106,139)(107,138)(108,137)
(109,136)(110,135)(111,123)(112,122)(113,132)(114,131)(115,130)(116,129)
(117,128)(118,127)(119,126)(120,125)(121,124)(155,233)(156,232)(157,242)
(158,241)(159,240)(160,239)(161,238)(162,237)(163,236)(164,235)(165,234)
(166,299)(167,298)(168,308)(169,307)(170,306)(171,305)(172,304)(173,303)
(174,302)(175,301)(176,300)(177,288)(178,287)(179,297)(180,296)(181,295)
(182,294)(183,293)(184,292)(185,291)(186,290)(187,289)(188,277)(189,276)
(190,286)(191,285)(192,284)(193,283)(194,282)(195,281)(196,280)(197,279)
(198,278)(199,266)(200,265)(201,275)(202,274)(203,273)(204,272)(205,271)
(206,270)(207,269)(208,268)(209,267)(210,255)(211,254)(212,264)(213,263)
(214,262)(215,261)(216,260)(217,259)(218,258)(219,257)(220,256)(221,244)
(222,243)(223,253)(224,252)(225,251)(226,250)(227,249)(228,248)(229,247)
(230,246)(231,245);
s2 := Sym(308)!( 1,166)( 2,167)( 3,168)( 4,169)( 5,170)( 6,171)( 7,172)
( 8,173)( 9,174)( 10,175)( 11,176)( 12,155)( 13,156)( 14,157)( 15,158)
( 16,159)( 17,160)( 18,161)( 19,162)( 20,163)( 21,164)( 22,165)( 23,221)
( 24,222)( 25,223)( 26,224)( 27,225)( 28,226)( 29,227)( 30,228)( 31,229)
( 32,230)( 33,231)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)
( 40,216)( 41,217)( 42,218)( 43,219)( 44,220)( 45,199)( 46,200)( 47,201)
( 48,202)( 49,203)( 50,204)( 51,205)( 52,206)( 53,207)( 54,208)( 55,209)
( 56,188)( 57,189)( 58,190)( 59,191)( 60,192)( 61,193)( 62,194)( 63,195)
( 64,196)( 65,197)( 66,198)( 67,177)( 68,178)( 69,179)( 70,180)( 71,181)
( 72,182)( 73,183)( 74,184)( 75,185)( 76,186)( 77,187)( 78,243)( 79,244)
( 80,245)( 81,246)( 82,247)( 83,248)( 84,249)( 85,250)( 86,251)( 87,252)
( 88,253)( 89,232)( 90,233)( 91,234)( 92,235)( 93,236)( 94,237)( 95,238)
( 96,239)( 97,240)( 98,241)( 99,242)(100,298)(101,299)(102,300)(103,301)
(104,302)(105,303)(106,304)(107,305)(108,306)(109,307)(110,308)(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)(133,265)(134,266)(135,267)
(136,268)(137,269)(138,270)(139,271)(140,272)(141,273)(142,274)(143,275)
(144,254)(145,255)(146,256)(147,257)(148,258)(149,259)(150,260)(151,261)
(152,262)(153,263)(154,264);
poly := sub<Sym(308)|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 >;
References : None.
to this polytope