Polytope of Type {49,14}

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

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