Polytope of Type {44,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,14}*1232
Also Known As : {44,14|2}. if this polytope has another name.
Group : SmallGroup(1232,98)
Rank : 3
Schlafli Type : {44,14}
Number of vertices, edges, etc : 44, 308, 14
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 : {44,2}*176
11-fold quotients : {4,14}*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 : {4,2}*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)(155,232)(156,242)
(157,241)(158,240)(159,239)(160,238)(161,237)(162,236)(163,235)(164,234)
(165,233)(166,243)(167,253)(168,252)(169,251)(170,250)(171,249)(172,248)
(173,247)(174,246)(175,245)(176,244)(177,254)(178,264)(179,263)(180,262)
(181,261)(182,260)(183,259)(184,258)(185,257)(186,256)(187,255)(188,265)
(189,275)(190,274)(191,273)(192,272)(193,271)(194,270)(195,269)(196,268)
(197,267)(198,266)(199,276)(200,286)(201,285)(202,284)(203,283)(204,282)
(205,281)(206,280)(207,279)(208,278)(209,277)(210,287)(211,297)(212,296)
(213,295)(214,294)(215,293)(216,292)(217,291)(218,290)(219,289)(220,288)
(221,298)(222,308)(223,307)(224,306)(225,305)(226,304)(227,303)(228,302)
(229,301)(230,300)(231,299);;
s1 := ( 1,156)( 2,155)( 3,165)( 4,164)( 5,163)( 6,162)( 7,161)( 8,160)
( 9,159)( 10,158)( 11,157)( 12,222)( 13,221)( 14,231)( 15,230)( 16,229)
( 17,228)( 18,227)( 19,226)( 20,225)( 21,224)( 22,223)( 23,211)( 24,210)
( 25,220)( 26,219)( 27,218)( 28,217)( 29,216)( 30,215)( 31,214)( 32,213)
( 33,212)( 34,200)( 35,199)( 36,209)( 37,208)( 38,207)( 39,206)( 40,205)
( 41,204)( 42,203)( 43,202)( 44,201)( 45,189)( 46,188)( 47,198)( 48,197)
( 49,196)( 50,195)( 51,194)( 52,193)( 53,192)( 54,191)( 55,190)( 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)( 78,233)( 79,232)( 80,242)
( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)( 88,234)
( 89,299)( 90,298)( 91,308)( 92,307)( 93,306)( 94,305)( 95,304)( 96,303)
( 97,302)( 98,301)( 99,300)(100,288)(101,287)(102,297)(103,296)(104,295)
(105,294)(106,293)(107,292)(108,291)(109,290)(110,289)(111,277)(112,276)
(113,286)(114,285)(115,284)(116,283)(117,282)(118,281)(119,280)(120,279)
(121,278)(122,266)(123,265)(124,275)(125,274)(126,273)(127,272)(128,271)
(129,270)(130,269)(131,268)(132,267)(133,255)(134,254)(135,264)(136,263)
(137,262)(138,261)(139,260)(140,259)(141,258)(142,257)(143,256)(144,244)
(145,243)(146,253)(147,252)(148,251)(149,250)(150,249)(151,248)(152,247)
(153,246)(154,245);;
s2 := ( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 16)( 6, 17)( 7, 18)( 8, 19)
( 9, 20)( 10, 21)( 11, 22)( 23, 67)( 24, 68)( 25, 69)( 26, 70)( 27, 71)
( 28, 72)( 29, 73)( 30, 74)( 31, 75)( 32, 76)( 33, 77)( 34, 56)( 35, 57)
( 36, 58)( 37, 59)( 38, 60)( 39, 61)( 40, 62)( 41, 63)( 42, 64)( 43, 65)
( 44, 66)( 78, 89)( 79, 90)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)
( 85, 96)( 86, 97)( 87, 98)( 88, 99)(100,144)(101,145)(102,146)(103,147)
(104,148)(105,149)(106,150)(107,151)(108,152)(109,153)(110,154)(111,133)
(112,134)(113,135)(114,136)(115,137)(116,138)(117,139)(118,140)(119,141)
(120,142)(121,143)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)
(161,172)(162,173)(163,174)(164,175)(165,176)(177,221)(178,222)(179,223)
(180,224)(181,225)(182,226)(183,227)(184,228)(185,229)(186,230)(187,231)
(188,210)(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)(195,217)
(196,218)(197,219)(198,220)(232,243)(233,244)(234,245)(235,246)(236,247)
(237,248)(238,249)(239,250)(240,251)(241,252)(242,253)(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);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!( 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)(155,232)
(156,242)(157,241)(158,240)(159,239)(160,238)(161,237)(162,236)(163,235)
(164,234)(165,233)(166,243)(167,253)(168,252)(169,251)(170,250)(171,249)
(172,248)(173,247)(174,246)(175,245)(176,244)(177,254)(178,264)(179,263)
(180,262)(181,261)(182,260)(183,259)(184,258)(185,257)(186,256)(187,255)
(188,265)(189,275)(190,274)(191,273)(192,272)(193,271)(194,270)(195,269)
(196,268)(197,267)(198,266)(199,276)(200,286)(201,285)(202,284)(203,283)
(204,282)(205,281)(206,280)(207,279)(208,278)(209,277)(210,287)(211,297)
(212,296)(213,295)(214,294)(215,293)(216,292)(217,291)(218,290)(219,289)
(220,288)(221,298)(222,308)(223,307)(224,306)(225,305)(226,304)(227,303)
(228,302)(229,301)(230,300)(231,299);
s1 := Sym(308)!( 1,156)( 2,155)( 3,165)( 4,164)( 5,163)( 6,162)( 7,161)
( 8,160)( 9,159)( 10,158)( 11,157)( 12,222)( 13,221)( 14,231)( 15,230)
( 16,229)( 17,228)( 18,227)( 19,226)( 20,225)( 21,224)( 22,223)( 23,211)
( 24,210)( 25,220)( 26,219)( 27,218)( 28,217)( 29,216)( 30,215)( 31,214)
( 32,213)( 33,212)( 34,200)( 35,199)( 36,209)( 37,208)( 38,207)( 39,206)
( 40,205)( 41,204)( 42,203)( 43,202)( 44,201)( 45,189)( 46,188)( 47,198)
( 48,197)( 49,196)( 50,195)( 51,194)( 52,193)( 53,192)( 54,191)( 55,190)
( 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)( 78,233)( 79,232)
( 80,242)( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)
( 88,234)( 89,299)( 90,298)( 91,308)( 92,307)( 93,306)( 94,305)( 95,304)
( 96,303)( 97,302)( 98,301)( 99,300)(100,288)(101,287)(102,297)(103,296)
(104,295)(105,294)(106,293)(107,292)(108,291)(109,290)(110,289)(111,277)
(112,276)(113,286)(114,285)(115,284)(116,283)(117,282)(118,281)(119,280)
(120,279)(121,278)(122,266)(123,265)(124,275)(125,274)(126,273)(127,272)
(128,271)(129,270)(130,269)(131,268)(132,267)(133,255)(134,254)(135,264)
(136,263)(137,262)(138,261)(139,260)(140,259)(141,258)(142,257)(143,256)
(144,244)(145,243)(146,253)(147,252)(148,251)(149,250)(150,249)(151,248)
(152,247)(153,246)(154,245);
s2 := Sym(308)!( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 16)( 6, 17)( 7, 18)
( 8, 19)( 9, 20)( 10, 21)( 11, 22)( 23, 67)( 24, 68)( 25, 69)( 26, 70)
( 27, 71)( 28, 72)( 29, 73)( 30, 74)( 31, 75)( 32, 76)( 33, 77)( 34, 56)
( 35, 57)( 36, 58)( 37, 59)( 38, 60)( 39, 61)( 40, 62)( 41, 63)( 42, 64)
( 43, 65)( 44, 66)( 78, 89)( 79, 90)( 80, 91)( 81, 92)( 82, 93)( 83, 94)
( 84, 95)( 85, 96)( 86, 97)( 87, 98)( 88, 99)(100,144)(101,145)(102,146)
(103,147)(104,148)(105,149)(106,150)(107,151)(108,152)(109,153)(110,154)
(111,133)(112,134)(113,135)(114,136)(115,137)(116,138)(117,139)(118,140)
(119,141)(120,142)(121,143)(155,166)(156,167)(157,168)(158,169)(159,170)
(160,171)(161,172)(162,173)(163,174)(164,175)(165,176)(177,221)(178,222)
(179,223)(180,224)(181,225)(182,226)(183,227)(184,228)(185,229)(186,230)
(187,231)(188,210)(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)
(195,217)(196,218)(197,219)(198,220)(232,243)(233,244)(234,245)(235,246)
(236,247)(237,248)(238,249)(239,250)(240,251)(241,252)(242,253)(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);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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