Polytope of Type {70,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {70,14}*1960a
if this polytope has a name.
Group : SmallGroup(1960,126)
Rank : 3
Schlafli Type : {70,14}
Number of vertices, edges, etc : 70, 490, 14
Order of s₀s₁s₂ : 70
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {14,14}*392b
   7-fold quotients : {10,14}*280
   10-fold quotients : {14,7}*196
   35-fold quotients : {2,14}*56
   49-fold quotients : {10,2}*40
   70-fold quotients : {2,7}*28
   98-fold quotients : {5,2}*20
   245-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 36)
( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)( 23, 30)
( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 50,197)( 51,198)( 52,199)
( 53,200)( 54,201)( 55,202)( 56,203)( 57,239)( 58,240)( 59,241)( 60,242)
( 61,243)( 62,244)( 63,245)( 64,232)( 65,233)( 66,234)( 67,235)( 68,236)
( 69,237)( 70,238)( 71,225)( 72,226)( 73,227)( 74,228)( 75,229)( 76,230)
( 77,231)( 78,218)( 79,219)( 80,220)( 81,221)( 82,222)( 83,223)( 84,224)
( 85,211)( 86,212)( 87,213)( 88,214)( 89,215)( 90,216)( 91,217)( 92,204)
( 93,205)( 94,206)( 95,207)( 96,208)( 97,209)( 98,210)( 99,148)(100,149)
(101,150)(102,151)(103,152)(104,153)(105,154)(106,190)(107,191)(108,192)
(109,193)(110,194)(111,195)(112,196)(113,183)(114,184)(115,185)(116,186)
(117,187)(118,188)(119,189)(120,176)(121,177)(122,178)(123,179)(124,180)
(125,181)(126,182)(127,169)(128,170)(129,171)(130,172)(131,173)(132,174)
(133,175)(134,162)(135,163)(136,164)(137,165)(138,166)(139,167)(140,168)
(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161);;
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, 92)( 16, 98)
( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22, 85)( 23, 91)( 24, 90)
( 25, 89)( 26, 88)( 27, 87)( 28, 86)( 29, 78)( 30, 84)( 31, 83)( 32, 82)
( 33, 81)( 34, 80)( 35, 79)( 36, 71)( 37, 77)( 38, 76)( 39, 75)( 40, 74)
( 41, 73)( 42, 72)( 43, 64)( 44, 70)( 45, 69)( 46, 68)( 47, 67)( 48, 66)
( 49, 65)( 99,204)(100,210)(101,209)(102,208)(103,207)(104,206)(105,205)
(106,197)(107,203)(108,202)(109,201)(110,200)(111,199)(112,198)(113,239)
(114,245)(115,244)(116,243)(117,242)(118,241)(119,240)(120,232)(121,238)
(122,237)(123,236)(124,235)(125,234)(126,233)(127,225)(128,231)(129,230)
(130,229)(131,228)(132,227)(133,226)(134,218)(135,224)(136,223)(137,222)
(138,221)(139,220)(140,219)(141,211)(142,217)(143,216)(144,215)(145,214)
(146,213)(147,212)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)
(154,156)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)
(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(177,182)
(178,181)(179,180);;
s2 := (  1,  2)(  3,  7)(  4,  6)(  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, 51)( 52, 56)( 53, 55)( 57, 93)( 58, 92)( 59, 98)( 60, 97)( 61, 96)
( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)( 69, 88)
( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)
( 99,100)(101,105)(102,104)(106,142)(107,141)(108,147)(109,146)(110,145)
(111,144)(112,143)(113,135)(114,134)(115,140)(116,139)(117,138)(118,137)
(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)(126,129)
(148,149)(150,154)(151,153)(155,191)(156,190)(157,196)(158,195)(159,194)
(160,193)(161,192)(162,184)(163,183)(164,189)(165,188)(166,187)(167,186)
(168,185)(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)(175,178)
(197,198)(199,203)(200,202)(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);;
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*s0*s1*s2*s0*s1*s2*s1*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, 
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(245)!(  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)
( 15, 36)( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)
( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 50,197)( 51,198)
( 52,199)( 53,200)( 54,201)( 55,202)( 56,203)( 57,239)( 58,240)( 59,241)
( 60,242)( 61,243)( 62,244)( 63,245)( 64,232)( 65,233)( 66,234)( 67,235)
( 68,236)( 69,237)( 70,238)( 71,225)( 72,226)( 73,227)( 74,228)( 75,229)
( 76,230)( 77,231)( 78,218)( 79,219)( 80,220)( 81,221)( 82,222)( 83,223)
( 84,224)( 85,211)( 86,212)( 87,213)( 88,214)( 89,215)( 90,216)( 91,217)
( 92,204)( 93,205)( 94,206)( 95,207)( 96,208)( 97,209)( 98,210)( 99,148)
(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)(106,190)(107,191)
(108,192)(109,193)(110,194)(111,195)(112,196)(113,183)(114,184)(115,185)
(116,186)(117,187)(118,188)(119,189)(120,176)(121,177)(122,178)(123,179)
(124,180)(125,181)(126,182)(127,169)(128,170)(129,171)(130,172)(131,173)
(132,174)(133,175)(134,162)(135,163)(136,164)(137,165)(138,166)(139,167)
(140,168)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161);
s1 := Sym(245)!(  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, 92)
( 16, 98)( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22, 85)( 23, 91)
( 24, 90)( 25, 89)( 26, 88)( 27, 87)( 28, 86)( 29, 78)( 30, 84)( 31, 83)
( 32, 82)( 33, 81)( 34, 80)( 35, 79)( 36, 71)( 37, 77)( 38, 76)( 39, 75)
( 40, 74)( 41, 73)( 42, 72)( 43, 64)( 44, 70)( 45, 69)( 46, 68)( 47, 67)
( 48, 66)( 49, 65)( 99,204)(100,210)(101,209)(102,208)(103,207)(104,206)
(105,205)(106,197)(107,203)(108,202)(109,201)(110,200)(111,199)(112,198)
(113,239)(114,245)(115,244)(116,243)(117,242)(118,241)(119,240)(120,232)
(121,238)(122,237)(123,236)(124,235)(125,234)(126,233)(127,225)(128,231)
(129,230)(130,229)(131,228)(132,227)(133,226)(134,218)(135,224)(136,223)
(137,222)(138,221)(139,220)(140,219)(141,211)(142,217)(143,216)(144,215)
(145,214)(146,213)(147,212)(148,155)(149,161)(150,160)(151,159)(152,158)
(153,157)(154,156)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)
(168,191)(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)
(177,182)(178,181)(179,180);
s2 := Sym(245)!(  1,  2)(  3,  7)(  4,  6)(  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, 51)( 52, 56)( 53, 55)( 57, 93)( 58, 92)( 59, 98)( 60, 97)
( 61, 96)( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)
( 69, 88)( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)
( 77, 80)( 99,100)(101,105)(102,104)(106,142)(107,141)(108,147)(109,146)
(110,145)(111,144)(112,143)(113,135)(114,134)(115,140)(116,139)(117,138)
(118,137)(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)
(126,129)(148,149)(150,154)(151,153)(155,191)(156,190)(157,196)(158,195)
(159,194)(160,193)(161,192)(162,184)(163,183)(164,189)(165,188)(166,187)
(167,186)(168,185)(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)
(175,178)(197,198)(199,203)(200,202)(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);
poly := sub<Sym(245)|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*s0*s1*s2*s0*s1*s2*s1*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, 
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