Polytope of Type {14,49}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,49}*1372
if this polytope has a name.
Group : SmallGroup(1372,15)
Rank : 3
Schlafli Type : {14,49}
Number of vertices, edges, etc : 14, 343, 49
Order of s₀s₁s₂ : 98
Order of s₀s₁s₂s₁ : 14
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) :
   7-fold quotients : {2,49}*196, {14,7}*196
   49-fold quotients : {2,7}*28
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 50,295)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)( 56,301)( 57,302)
( 58,303)( 59,304)( 60,305)( 61,306)( 62,307)( 63,308)( 64,309)( 65,310)
( 66,311)( 67,312)( 68,313)( 69,314)( 70,315)( 71,316)( 72,317)( 73,318)
( 74,319)( 75,320)( 76,321)( 77,322)( 78,323)( 79,324)( 80,325)( 81,326)
( 82,327)( 83,328)( 84,329)( 85,330)( 86,331)( 87,332)( 88,333)( 89,334)
( 90,335)( 91,336)( 92,337)( 93,338)( 94,339)( 95,340)( 96,341)( 97,342)
( 98,343)( 99,246)(100,247)(101,248)(102,249)(103,250)(104,251)(105,252)
(106,253)(107,254)(108,255)(109,256)(110,257)(111,258)(112,259)(113,260)
(114,261)(115,262)(116,263)(117,264)(118,265)(119,266)(120,267)(121,268)
(122,269)(123,270)(124,271)(125,272)(126,273)(127,274)(128,275)(129,276)
(130,277)(131,278)(132,279)(133,280)(134,281)(135,282)(136,283)(137,284)
(138,285)(139,286)(140,287)(141,288)(142,289)(143,290)(144,291)(145,292)
(146,293)(147,294)(148,197)(149,198)(150,199)(151,200)(152,201)(153,202)
(154,203)(155,204)(156,205)(157,206)(158,207)(159,208)(160,209)(161,210)
(162,211)(163,212)(164,213)(165,214)(166,215)(167,216)(168,217)(169,218)
(170,219)(171,220)(172,221)(173,222)(174,223)(175,224)(176,225)(177,226)
(178,227)(179,228)(180,229)(181,230)(182,231)(183,232)(184,233)(185,234)
(186,235)(187,236)(188,237)(189,238)(190,239)(191,240)(192,241)(193,242)
(194,243)(195,244)(196,245);;
s1 := (  1, 50)(  2, 56)(  3, 55)(  4, 54)(  5, 53)(  6, 52)(  7, 51)(  8, 93)
(  9, 92)( 10, 98)( 11, 97)( 12, 96)( 13, 95)( 14, 94)( 15, 86)( 16, 85)
( 17, 91)( 18, 90)( 19, 89)( 20, 88)( 21, 87)( 22, 79)( 23, 78)( 24, 84)
( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 72)( 30, 71)( 31, 77)( 32, 76)
( 33, 75)( 34, 74)( 35, 73)( 36, 65)( 37, 64)( 38, 70)( 39, 69)( 40, 68)
( 41, 67)( 42, 66)( 43, 58)( 44, 57)( 45, 63)( 46, 62)( 47, 61)( 48, 60)
( 49, 59)( 99,295)(100,301)(101,300)(102,299)(103,298)(104,297)(105,296)
(106,338)(107,337)(108,343)(109,342)(110,341)(111,340)(112,339)(113,331)
(114,330)(115,336)(116,335)(117,334)(118,333)(119,332)(120,324)(121,323)
(122,329)(123,328)(124,327)(125,326)(126,325)(127,317)(128,316)(129,322)
(130,321)(131,320)(132,319)(133,318)(134,310)(135,309)(136,315)(137,314)
(138,313)(139,312)(140,311)(141,303)(142,302)(143,308)(144,307)(145,306)
(146,305)(147,304)(148,246)(149,252)(150,251)(151,250)(152,249)(153,248)
(154,247)(155,289)(156,288)(157,294)(158,293)(159,292)(160,291)(161,290)
(162,282)(163,281)(164,287)(165,286)(166,285)(167,284)(168,283)(169,275)
(170,274)(171,280)(172,279)(173,278)(174,277)(175,276)(176,268)(177,267)
(178,273)(179,272)(180,271)(181,270)(182,269)(183,261)(184,260)(185,266)
(186,265)(187,264)(188,263)(189,262)(190,254)(191,253)(192,259)(193,258)
(194,257)(195,256)(196,255)(198,203)(199,202)(200,201)(204,240)(205,239)
(206,245)(207,244)(208,243)(209,242)(210,241)(211,233)(212,232)(213,238)
(214,237)(215,236)(216,235)(217,234)(218,226)(219,225)(220,231)(221,230)
(222,229)(223,228)(224,227);;
s2 := (  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 15, 44)
( 16, 43)( 17, 49)( 18, 48)( 19, 47)( 20, 46)( 21, 45)( 22, 37)( 23, 36)
( 24, 42)( 25, 41)( 26, 40)( 27, 39)( 28, 38)( 29, 30)( 31, 35)( 32, 34)
( 50,302)( 51,308)( 52,307)( 53,306)( 54,305)( 55,304)( 56,303)( 57,295)
( 58,301)( 59,300)( 60,299)( 61,298)( 62,297)( 63,296)( 64,338)( 65,337)
( 66,343)( 67,342)( 68,341)( 69,340)( 70,339)( 71,331)( 72,330)( 73,336)
( 74,335)( 75,334)( 76,333)( 77,332)( 78,324)( 79,323)( 80,329)( 81,328)
( 82,327)( 83,326)( 84,325)( 85,317)( 86,316)( 87,322)( 88,321)( 89,320)
( 90,319)( 91,318)( 92,310)( 93,309)( 94,315)( 95,314)( 96,313)( 97,312)
( 98,311)( 99,253)(100,259)(101,258)(102,257)(103,256)(104,255)(105,254)
(106,246)(107,252)(108,251)(109,250)(110,249)(111,248)(112,247)(113,289)
(114,288)(115,294)(116,293)(117,292)(118,291)(119,290)(120,282)(121,281)
(122,287)(123,286)(124,285)(125,284)(126,283)(127,275)(128,274)(129,280)
(130,279)(131,278)(132,277)(133,276)(134,268)(135,267)(136,273)(137,272)
(138,271)(139,270)(140,269)(141,261)(142,260)(143,266)(144,265)(145,264)
(146,263)(147,262)(148,204)(149,210)(150,209)(151,208)(152,207)(153,206)
(154,205)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)
(162,240)(163,239)(164,245)(165,244)(166,243)(167,242)(168,241)(169,233)
(170,232)(171,238)(172,237)(173,236)(174,235)(175,234)(176,226)(177,225)
(178,231)(179,230)(180,229)(181,228)(182,227)(183,219)(184,218)(185,224)
(186,223)(187,222)(188,221)(189,220)(190,212)(191,211)(192,217)(193,216)
(194,215)(195,214)(196,213);;
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, s2*s0*s1*s0*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, 
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*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(343)!( 50,295)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)( 56,301)
( 57,302)( 58,303)( 59,304)( 60,305)( 61,306)( 62,307)( 63,308)( 64,309)
( 65,310)( 66,311)( 67,312)( 68,313)( 69,314)( 70,315)( 71,316)( 72,317)
( 73,318)( 74,319)( 75,320)( 76,321)( 77,322)( 78,323)( 79,324)( 80,325)
( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,331)( 87,332)( 88,333)
( 89,334)( 90,335)( 91,336)( 92,337)( 93,338)( 94,339)( 95,340)( 96,341)
( 97,342)( 98,343)( 99,246)(100,247)(101,248)(102,249)(103,250)(104,251)
(105,252)(106,253)(107,254)(108,255)(109,256)(110,257)(111,258)(112,259)
(113,260)(114,261)(115,262)(116,263)(117,264)(118,265)(119,266)(120,267)
(121,268)(122,269)(123,270)(124,271)(125,272)(126,273)(127,274)(128,275)
(129,276)(130,277)(131,278)(132,279)(133,280)(134,281)(135,282)(136,283)
(137,284)(138,285)(139,286)(140,287)(141,288)(142,289)(143,290)(144,291)
(145,292)(146,293)(147,294)(148,197)(149,198)(150,199)(151,200)(152,201)
(153,202)(154,203)(155,204)(156,205)(157,206)(158,207)(159,208)(160,209)
(161,210)(162,211)(163,212)(164,213)(165,214)(166,215)(167,216)(168,217)
(169,218)(170,219)(171,220)(172,221)(173,222)(174,223)(175,224)(176,225)
(177,226)(178,227)(179,228)(180,229)(181,230)(182,231)(183,232)(184,233)
(185,234)(186,235)(187,236)(188,237)(189,238)(190,239)(191,240)(192,241)
(193,242)(194,243)(195,244)(196,245);
s1 := Sym(343)!(  1, 50)(  2, 56)(  3, 55)(  4, 54)(  5, 53)(  6, 52)(  7, 51)
(  8, 93)(  9, 92)( 10, 98)( 11, 97)( 12, 96)( 13, 95)( 14, 94)( 15, 86)
( 16, 85)( 17, 91)( 18, 90)( 19, 89)( 20, 88)( 21, 87)( 22, 79)( 23, 78)
( 24, 84)( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 72)( 30, 71)( 31, 77)
( 32, 76)( 33, 75)( 34, 74)( 35, 73)( 36, 65)( 37, 64)( 38, 70)( 39, 69)
( 40, 68)( 41, 67)( 42, 66)( 43, 58)( 44, 57)( 45, 63)( 46, 62)( 47, 61)
( 48, 60)( 49, 59)( 99,295)(100,301)(101,300)(102,299)(103,298)(104,297)
(105,296)(106,338)(107,337)(108,343)(109,342)(110,341)(111,340)(112,339)
(113,331)(114,330)(115,336)(116,335)(117,334)(118,333)(119,332)(120,324)
(121,323)(122,329)(123,328)(124,327)(125,326)(126,325)(127,317)(128,316)
(129,322)(130,321)(131,320)(132,319)(133,318)(134,310)(135,309)(136,315)
(137,314)(138,313)(139,312)(140,311)(141,303)(142,302)(143,308)(144,307)
(145,306)(146,305)(147,304)(148,246)(149,252)(150,251)(151,250)(152,249)
(153,248)(154,247)(155,289)(156,288)(157,294)(158,293)(159,292)(160,291)
(161,290)(162,282)(163,281)(164,287)(165,286)(166,285)(167,284)(168,283)
(169,275)(170,274)(171,280)(172,279)(173,278)(174,277)(175,276)(176,268)
(177,267)(178,273)(179,272)(180,271)(181,270)(182,269)(183,261)(184,260)
(185,266)(186,265)(187,264)(188,263)(189,262)(190,254)(191,253)(192,259)
(193,258)(194,257)(195,256)(196,255)(198,203)(199,202)(200,201)(204,240)
(205,239)(206,245)(207,244)(208,243)(209,242)(210,241)(211,233)(212,232)
(213,238)(214,237)(215,236)(216,235)(217,234)(218,226)(219,225)(220,231)
(221,230)(222,229)(223,228)(224,227);
s2 := Sym(343)!(  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)
( 15, 44)( 16, 43)( 17, 49)( 18, 48)( 19, 47)( 20, 46)( 21, 45)( 22, 37)
( 23, 36)( 24, 42)( 25, 41)( 26, 40)( 27, 39)( 28, 38)( 29, 30)( 31, 35)
( 32, 34)( 50,302)( 51,308)( 52,307)( 53,306)( 54,305)( 55,304)( 56,303)
( 57,295)( 58,301)( 59,300)( 60,299)( 61,298)( 62,297)( 63,296)( 64,338)
( 65,337)( 66,343)( 67,342)( 68,341)( 69,340)( 70,339)( 71,331)( 72,330)
( 73,336)( 74,335)( 75,334)( 76,333)( 77,332)( 78,324)( 79,323)( 80,329)
( 81,328)( 82,327)( 83,326)( 84,325)( 85,317)( 86,316)( 87,322)( 88,321)
( 89,320)( 90,319)( 91,318)( 92,310)( 93,309)( 94,315)( 95,314)( 96,313)
( 97,312)( 98,311)( 99,253)(100,259)(101,258)(102,257)(103,256)(104,255)
(105,254)(106,246)(107,252)(108,251)(109,250)(110,249)(111,248)(112,247)
(113,289)(114,288)(115,294)(116,293)(117,292)(118,291)(119,290)(120,282)
(121,281)(122,287)(123,286)(124,285)(125,284)(126,283)(127,275)(128,274)
(129,280)(130,279)(131,278)(132,277)(133,276)(134,268)(135,267)(136,273)
(137,272)(138,271)(139,270)(140,269)(141,261)(142,260)(143,266)(144,265)
(145,264)(146,263)(147,262)(148,204)(149,210)(150,209)(151,208)(152,207)
(153,206)(154,205)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)
(161,198)(162,240)(163,239)(164,245)(165,244)(166,243)(167,242)(168,241)
(169,233)(170,232)(171,238)(172,237)(173,236)(174,235)(175,234)(176,226)
(177,225)(178,231)(179,230)(180,229)(181,228)(182,227)(183,219)(184,218)
(185,224)(186,223)(187,222)(188,221)(189,220)(190,212)(191,211)(192,217)
(193,216)(194,215)(195,214)(196,213);
poly := sub<Sym(343)|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, s2*s0*s1*s0*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, 
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*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