Polytope of Type {35,14,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {35,14,2}*1960
if this polytope has a name.
Group : SmallGroup(1960,137)
Rank : 4
Schlafli Type : {35,14,2}
Number of vertices, edges, etc : 35, 245, 14, 2
Order of s₀s₁s₂s₃ : 70
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {7,14,2}*392
   7-fold quotients : {35,2,2}*280
   35-fold quotients : {7,2,2}*56
   49-fold quotients : {5,2,2}*40
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)
( 50,197)( 51,203)( 52,202)( 53,201)( 54,200)( 55,199)( 56,198)( 57,239)
( 58,245)( 59,244)( 60,243)( 61,242)( 62,241)( 63,240)( 64,232)( 65,238)
( 66,237)( 67,236)( 68,235)( 69,234)( 70,233)( 71,225)( 72,231)( 73,230)
( 74,229)( 75,228)( 76,227)( 77,226)( 78,218)( 79,224)( 80,223)( 81,222)
( 82,221)( 83,220)( 84,219)( 85,211)( 86,217)( 87,216)( 88,215)( 89,214)
( 90,213)( 91,212)( 92,204)( 93,210)( 94,209)( 95,208)( 96,207)( 97,206)
( 98,205)( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)
(106,190)(107,196)(108,195)(109,194)(110,193)(111,192)(112,191)(113,183)
(114,189)(115,188)(116,187)(117,186)(118,185)(119,184)(120,176)(121,182)
(122,181)(123,180)(124,179)(125,178)(126,177)(127,169)(128,175)(129,174)
(130,173)(131,172)(132,171)(133,170)(134,162)(135,168)(136,167)(137,166)
(138,165)(139,164)(140,163)(141,155)(142,161)(143,160)(144,159)(145,158)
(146,157)(147,156);;
s1 := (  1, 58)(  2, 57)(  3, 63)(  4, 62)(  5, 61)(  6, 60)(  7, 59)(  8, 51)
(  9, 50)( 10, 56)( 11, 55)( 12, 54)( 13, 53)( 14, 52)( 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)( 99,205)(100,204)(101,210)(102,209)(103,208)(104,207)(105,206)
(106,198)(107,197)(108,203)(109,202)(110,201)(111,200)(112,199)(113,240)
(114,239)(115,245)(116,244)(117,243)(118,242)(119,241)(120,233)(121,232)
(122,238)(123,237)(124,236)(125,235)(126,234)(127,226)(128,225)(129,231)
(130,230)(131,229)(132,228)(133,227)(134,219)(135,218)(136,224)(137,223)
(138,222)(139,221)(140,220)(141,212)(142,211)(143,217)(144,216)(145,215)
(146,214)(147,213)(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)
(154,157)(162,191)(163,190)(164,196)(165,195)(166,194)(167,193)(168,192)
(169,184)(170,183)(171,189)(172,188)(173,187)(174,186)(175,185)(176,177)
(178,182)(179,181);;
s2 := (  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)( 57, 92)( 58, 93)( 59, 94)
( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)( 67, 88)
( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)
( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)(111,146)
(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)
(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)(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)(204,239)(205,240)(206,241)(207,242)
(208,243)(209,244)(210,245)(211,232)(212,233)(213,234)(214,235)(215,236)
(216,237)(217,238)(218,225)(219,226)(220,227)(221,228)(222,229)(223,230)
(224,231);;
s3 := (246,247);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(247)!(  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)( 50,197)( 51,203)( 52,202)( 53,201)( 54,200)( 55,199)( 56,198)
( 57,239)( 58,245)( 59,244)( 60,243)( 61,242)( 62,241)( 63,240)( 64,232)
( 65,238)( 66,237)( 67,236)( 68,235)( 69,234)( 70,233)( 71,225)( 72,231)
( 73,230)( 74,229)( 75,228)( 76,227)( 77,226)( 78,218)( 79,224)( 80,223)
( 81,222)( 82,221)( 83,220)( 84,219)( 85,211)( 86,217)( 87,216)( 88,215)
( 89,214)( 90,213)( 91,212)( 92,204)( 93,210)( 94,209)( 95,208)( 96,207)
( 97,206)( 98,205)( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)
(105,149)(106,190)(107,196)(108,195)(109,194)(110,193)(111,192)(112,191)
(113,183)(114,189)(115,188)(116,187)(117,186)(118,185)(119,184)(120,176)
(121,182)(122,181)(123,180)(124,179)(125,178)(126,177)(127,169)(128,175)
(129,174)(130,173)(131,172)(132,171)(133,170)(134,162)(135,168)(136,167)
(137,166)(138,165)(139,164)(140,163)(141,155)(142,161)(143,160)(144,159)
(145,158)(146,157)(147,156);
s1 := Sym(247)!(  1, 58)(  2, 57)(  3, 63)(  4, 62)(  5, 61)(  6, 60)(  7, 59)
(  8, 51)(  9, 50)( 10, 56)( 11, 55)( 12, 54)( 13, 53)( 14, 52)( 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)( 99,205)(100,204)(101,210)(102,209)(103,208)(104,207)
(105,206)(106,198)(107,197)(108,203)(109,202)(110,201)(111,200)(112,199)
(113,240)(114,239)(115,245)(116,244)(117,243)(118,242)(119,241)(120,233)
(121,232)(122,238)(123,237)(124,236)(125,235)(126,234)(127,226)(128,225)
(129,231)(130,230)(131,229)(132,228)(133,227)(134,219)(135,218)(136,224)
(137,223)(138,222)(139,221)(140,220)(141,212)(142,211)(143,217)(144,216)
(145,215)(146,214)(147,213)(148,156)(149,155)(150,161)(151,160)(152,159)
(153,158)(154,157)(162,191)(163,190)(164,196)(165,195)(166,194)(167,193)
(168,192)(169,184)(170,183)(171,189)(172,188)(173,187)(174,186)(175,185)
(176,177)(178,182)(179,181);
s2 := Sym(247)!(  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)( 57, 92)( 58, 93)
( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)
( 67, 88)( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)
( 75, 82)( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)
(111,146)(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)
(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)
(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)(204,239)(205,240)(206,241)
(207,242)(208,243)(209,244)(210,245)(211,232)(212,233)(213,234)(214,235)
(215,236)(216,237)(217,238)(218,225)(219,226)(220,227)(221,228)(222,229)
(223,230)(224,231);
s3 := Sym(247)!(246,247);
poly := sub<Sym(247)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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 >;

to this polytope