Polytope of Type {28,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,22}*1232
Also Known As : {28,22|2}. if this polytope has another name.
Group : SmallGroup(1232,97)
Rank : 3
Schlafli Type : {28,22}
Number of vertices, edges, etc : 28, 308, 22
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 : {14,22}*616
   7-fold quotients : {4,22}*176
   11-fold quotients : {28,2}*112
   14-fold quotients : {2,22}*88
   22-fold quotients : {14,2}*56
   28-fold quotients : {2,11}*44
   44-fold quotients : {7,2}*28
   77-fold quotients : {4,2}*16
   154-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 12, 67)( 13, 68)( 14, 69)( 15, 70)( 16, 71)( 17, 72)( 18, 73)( 19, 74)
( 20, 75)( 21, 76)( 22, 77)( 23, 56)( 24, 57)( 25, 58)( 26, 59)( 27, 60)
( 28, 61)( 29, 62)( 30, 63)( 31, 64)( 32, 65)( 33, 66)( 34, 45)( 35, 46)
( 36, 47)( 37, 48)( 38, 49)( 39, 50)( 40, 51)( 41, 52)( 42, 53)( 43, 54)
( 44, 55)( 89,144)( 90,145)( 91,146)( 92,147)( 93,148)( 94,149)( 95,150)
( 96,151)( 97,152)( 98,153)( 99,154)(100,133)(101,134)(102,135)(103,136)
(104,137)(105,138)(106,139)(107,140)(108,141)(109,142)(110,143)(111,122)
(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)(119,130)
(120,131)(121,132)(155,232)(156,233)(157,234)(158,235)(159,236)(160,237)
(161,238)(162,239)(163,240)(164,241)(165,242)(166,298)(167,299)(168,300)
(169,301)(170,302)(171,303)(172,304)(173,305)(174,306)(175,307)(176,308)
(177,287)(178,288)(179,289)(180,290)(181,291)(182,292)(183,293)(184,294)
(185,295)(186,296)(187,297)(188,276)(189,277)(190,278)(191,279)(192,280)
(193,281)(194,282)(195,283)(196,284)(197,285)(198,286)(199,265)(200,266)
(201,267)(202,268)(203,269)(204,270)(205,271)(206,272)(207,273)(208,274)
(209,275)(210,254)(211,255)(212,256)(213,257)(214,258)(215,259)(216,260)
(217,261)(218,262)(219,263)(220,264)(221,243)(222,244)(223,245)(224,246)
(225,247)(226,248)(227,249)(228,250)(229,251)(230,252)(231,253);;
s1 := (  1,166)(  2,176)(  3,175)(  4,174)(  5,173)(  6,172)(  7,171)(  8,170)
(  9,169)( 10,168)( 11,167)( 12,155)( 13,165)( 14,164)( 15,163)( 16,162)
( 17,161)( 18,160)( 19,159)( 20,158)( 21,157)( 22,156)( 23,221)( 24,231)
( 25,230)( 26,229)( 27,228)( 28,227)( 29,226)( 30,225)( 31,224)( 32,223)
( 33,222)( 34,210)( 35,220)( 36,219)( 37,218)( 38,217)( 39,216)( 40,215)
( 41,214)( 42,213)( 43,212)( 44,211)( 45,199)( 46,209)( 47,208)( 48,207)
( 49,206)( 50,205)( 51,204)( 52,203)( 53,202)( 54,201)( 55,200)( 56,188)
( 57,198)( 58,197)( 59,196)( 60,195)( 61,194)( 62,193)( 63,192)( 64,191)
( 65,190)( 66,189)( 67,177)( 68,187)( 69,186)( 70,185)( 71,184)( 72,183)
( 73,182)( 74,181)( 75,180)( 76,179)( 77,178)( 78,243)( 79,253)( 80,252)
( 81,251)( 82,250)( 83,249)( 84,248)( 85,247)( 86,246)( 87,245)( 88,244)
( 89,232)( 90,242)( 91,241)( 92,240)( 93,239)( 94,238)( 95,237)( 96,236)
( 97,235)( 98,234)( 99,233)(100,298)(101,308)(102,307)(103,306)(104,305)
(105,304)(106,303)(107,302)(108,301)(109,300)(110,299)(111,287)(112,297)
(113,296)(114,295)(115,294)(116,293)(117,292)(118,291)(119,290)(120,289)
(121,288)(122,276)(123,286)(124,285)(125,284)(126,283)(127,282)(128,281)
(129,280)(130,279)(131,278)(132,277)(133,265)(134,275)(135,274)(136,273)
(137,272)(138,271)(139,270)(140,269)(141,268)(142,267)(143,266)(144,254)
(145,264)(146,263)(147,262)(148,261)(149,260)(150,259)(151,258)(152,257)
(153,256)(154,255);;
s2 := (  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)
( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 46)( 47, 55)( 48, 54)( 49, 53)
( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 68)( 69, 77)
( 70, 76)( 71, 75)( 72, 74)( 78, 79)( 80, 88)( 81, 87)( 82, 86)( 83, 85)
( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)(103,109)
(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)(122,123)
(124,132)(125,131)(126,130)(127,129)(133,134)(135,143)(136,142)(137,141)
(138,140)(144,145)(146,154)(147,153)(148,152)(149,151)(155,156)(157,165)
(158,164)(159,163)(160,162)(166,167)(168,176)(169,175)(170,174)(171,173)
(177,178)(179,187)(180,186)(181,185)(182,184)(188,189)(190,198)(191,197)
(192,196)(193,195)(199,200)(201,209)(202,208)(203,207)(204,206)(210,211)
(212,220)(213,219)(214,218)(215,217)(221,222)(223,231)(224,230)(225,229)
(226,228)(232,233)(234,242)(235,241)(236,240)(237,239)(243,244)(245,253)
(246,252)(247,251)(248,250)(254,255)(256,264)(257,263)(258,262)(259,261)
(265,266)(267,275)(268,274)(269,273)(270,272)(276,277)(278,286)(279,285)
(280,284)(281,283)(287,288)(289,297)(290,296)(291,295)(292,294)(298,299)
(300,308)(301,307)(302,306)(303,305);;
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, 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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(308)!( 12, 67)( 13, 68)( 14, 69)( 15, 70)( 16, 71)( 17, 72)( 18, 73)
( 19, 74)( 20, 75)( 21, 76)( 22, 77)( 23, 56)( 24, 57)( 25, 58)( 26, 59)
( 27, 60)( 28, 61)( 29, 62)( 30, 63)( 31, 64)( 32, 65)( 33, 66)( 34, 45)
( 35, 46)( 36, 47)( 37, 48)( 38, 49)( 39, 50)( 40, 51)( 41, 52)( 42, 53)
( 43, 54)( 44, 55)( 89,144)( 90,145)( 91,146)( 92,147)( 93,148)( 94,149)
( 95,150)( 96,151)( 97,152)( 98,153)( 99,154)(100,133)(101,134)(102,135)
(103,136)(104,137)(105,138)(106,139)(107,140)(108,141)(109,142)(110,143)
(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)
(119,130)(120,131)(121,132)(155,232)(156,233)(157,234)(158,235)(159,236)
(160,237)(161,238)(162,239)(163,240)(164,241)(165,242)(166,298)(167,299)
(168,300)(169,301)(170,302)(171,303)(172,304)(173,305)(174,306)(175,307)
(176,308)(177,287)(178,288)(179,289)(180,290)(181,291)(182,292)(183,293)
(184,294)(185,295)(186,296)(187,297)(188,276)(189,277)(190,278)(191,279)
(192,280)(193,281)(194,282)(195,283)(196,284)(197,285)(198,286)(199,265)
(200,266)(201,267)(202,268)(203,269)(204,270)(205,271)(206,272)(207,273)
(208,274)(209,275)(210,254)(211,255)(212,256)(213,257)(214,258)(215,259)
(216,260)(217,261)(218,262)(219,263)(220,264)(221,243)(222,244)(223,245)
(224,246)(225,247)(226,248)(227,249)(228,250)(229,251)(230,252)(231,253);
s1 := Sym(308)!(  1,166)(  2,176)(  3,175)(  4,174)(  5,173)(  6,172)(  7,171)
(  8,170)(  9,169)( 10,168)( 11,167)( 12,155)( 13,165)( 14,164)( 15,163)
( 16,162)( 17,161)( 18,160)( 19,159)( 20,158)( 21,157)( 22,156)( 23,221)
( 24,231)( 25,230)( 26,229)( 27,228)( 28,227)( 29,226)( 30,225)( 31,224)
( 32,223)( 33,222)( 34,210)( 35,220)( 36,219)( 37,218)( 38,217)( 39,216)
( 40,215)( 41,214)( 42,213)( 43,212)( 44,211)( 45,199)( 46,209)( 47,208)
( 48,207)( 49,206)( 50,205)( 51,204)( 52,203)( 53,202)( 54,201)( 55,200)
( 56,188)( 57,198)( 58,197)( 59,196)( 60,195)( 61,194)( 62,193)( 63,192)
( 64,191)( 65,190)( 66,189)( 67,177)( 68,187)( 69,186)( 70,185)( 71,184)
( 72,183)( 73,182)( 74,181)( 75,180)( 76,179)( 77,178)( 78,243)( 79,253)
( 80,252)( 81,251)( 82,250)( 83,249)( 84,248)( 85,247)( 86,246)( 87,245)
( 88,244)( 89,232)( 90,242)( 91,241)( 92,240)( 93,239)( 94,238)( 95,237)
( 96,236)( 97,235)( 98,234)( 99,233)(100,298)(101,308)(102,307)(103,306)
(104,305)(105,304)(106,303)(107,302)(108,301)(109,300)(110,299)(111,287)
(112,297)(113,296)(114,295)(115,294)(116,293)(117,292)(118,291)(119,290)
(120,289)(121,288)(122,276)(123,286)(124,285)(125,284)(126,283)(127,282)
(128,281)(129,280)(130,279)(131,278)(132,277)(133,265)(134,275)(135,274)
(136,273)(137,272)(138,271)(139,270)(140,269)(141,268)(142,267)(143,266)
(144,254)(145,264)(146,263)(147,262)(148,261)(149,260)(150,259)(151,258)
(152,257)(153,256)(154,255);
s2 := Sym(308)!(  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)
( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 46)( 47, 55)( 48, 54)
( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 68)
( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 78, 79)( 80, 88)( 81, 87)( 82, 86)
( 83, 85)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)
(103,109)(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)
(122,123)(124,132)(125,131)(126,130)(127,129)(133,134)(135,143)(136,142)
(137,141)(138,140)(144,145)(146,154)(147,153)(148,152)(149,151)(155,156)
(157,165)(158,164)(159,163)(160,162)(166,167)(168,176)(169,175)(170,174)
(171,173)(177,178)(179,187)(180,186)(181,185)(182,184)(188,189)(190,198)
(191,197)(192,196)(193,195)(199,200)(201,209)(202,208)(203,207)(204,206)
(210,211)(212,220)(213,219)(214,218)(215,217)(221,222)(223,231)(224,230)
(225,229)(226,228)(232,233)(234,242)(235,241)(236,240)(237,239)(243,244)
(245,253)(246,252)(247,251)(248,250)(254,255)(256,264)(257,263)(258,262)
(259,261)(265,266)(267,275)(268,274)(269,273)(270,272)(276,277)(278,286)
(279,285)(280,284)(281,283)(287,288)(289,297)(290,296)(291,295)(292,294)
(298,299)(300,308)(301,307)(302,306)(303,305);
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, 
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 >;

References : None.
to this polytope