Polytope of Type {14,70}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,70}*1960a
if this polytope has a name.
Group : SmallGroup(1960,126)
Rank : 3
Schlafli Type : {14,70}
Number of vertices, edges, etc : 14, 490, 70
Order of s₀s₁s₂ : 70
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) :
   5-fold quotients : {14,14}*392c
   7-fold quotients : {14,10}*280
   10-fold quotients : {7,14}*196
   35-fold quotients : {14,2}*56
   49-fold quotients : {2,10}*40
   70-fold quotients : {7,2}*28
   98-fold quotients : {2,5}*20
   245-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope