Polytope of Type {2,35,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,35,14}*1960
if this polytope has a name.
Group : SmallGroup(1960,137)
Rank : 4
Schlafli Type : {2,35,14}
Number of vertices, edges, etc : 2, 35, 245, 14
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 : {2,7,14}*392
   7-fold quotients : {2,35,2}*280
   35-fold quotients : {2,7,2}*56
   49-fold quotients : {2,5,2}*40
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 10, 45)( 11, 51)( 12, 50)( 13, 49)( 14, 48)
( 15, 47)( 16, 46)( 17, 38)( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)
( 23, 39)( 24, 31)( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)( 30, 32)
( 52,199)( 53,205)( 54,204)( 55,203)( 56,202)( 57,201)( 58,200)( 59,241)
( 60,247)( 61,246)( 62,245)( 63,244)( 64,243)( 65,242)( 66,234)( 67,240)
( 68,239)( 69,238)( 70,237)( 71,236)( 72,235)( 73,227)( 74,233)( 75,232)
( 76,231)( 77,230)( 78,229)( 79,228)( 80,220)( 81,226)( 82,225)( 83,224)
( 84,223)( 85,222)( 86,221)( 87,213)( 88,219)( 89,218)( 90,217)( 91,216)
( 92,215)( 93,214)( 94,206)( 95,212)( 96,211)( 97,210)( 98,209)( 99,208)
(100,207)(101,150)(102,156)(103,155)(104,154)(105,153)(106,152)(107,151)
(108,192)(109,198)(110,197)(111,196)(112,195)(113,194)(114,193)(115,185)
(116,191)(117,190)(118,189)(119,188)(120,187)(121,186)(122,178)(123,184)
(124,183)(125,182)(126,181)(127,180)(128,179)(129,171)(130,177)(131,176)
(132,175)(133,174)(134,173)(135,172)(136,164)(137,170)(138,169)(139,168)
(140,167)(141,166)(142,165)(143,157)(144,163)(145,162)(146,161)(147,160)
(148,159)(149,158);;
s2 := (  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)( 10, 53)
( 11, 52)( 12, 58)( 13, 57)( 14, 56)( 15, 55)( 16, 54)( 17, 95)( 18, 94)
( 19,100)( 20, 99)( 21, 98)( 22, 97)( 23, 96)( 24, 88)( 25, 87)( 26, 93)
( 27, 92)( 28, 91)( 29, 90)( 30, 89)( 31, 81)( 32, 80)( 33, 86)( 34, 85)
( 35, 84)( 36, 83)( 37, 82)( 38, 74)( 39, 73)( 40, 79)( 41, 78)( 42, 77)
( 43, 76)( 44, 75)( 45, 67)( 46, 66)( 47, 72)( 48, 71)( 49, 70)( 50, 69)
( 51, 68)(101,207)(102,206)(103,212)(104,211)(105,210)(106,209)(107,208)
(108,200)(109,199)(110,205)(111,204)(112,203)(113,202)(114,201)(115,242)
(116,241)(117,247)(118,246)(119,245)(120,244)(121,243)(122,235)(123,234)
(124,240)(125,239)(126,238)(127,237)(128,236)(129,228)(130,227)(131,233)
(132,232)(133,231)(134,230)(135,229)(136,221)(137,220)(138,226)(139,225)
(140,224)(141,223)(142,222)(143,214)(144,213)(145,219)(146,218)(147,217)
(148,216)(149,215)(150,158)(151,157)(152,163)(153,162)(154,161)(155,160)
(156,159)(164,193)(165,192)(166,198)(167,197)(168,196)(169,195)(170,194)
(171,186)(172,185)(173,191)(174,190)(175,189)(176,188)(177,187)(178,179)
(180,184)(181,183);;
s3 := ( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 50)( 16, 51)( 17, 38)
( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 43)( 23, 44)( 24, 31)( 25, 32)
( 26, 33)( 27, 34)( 28, 35)( 29, 36)( 30, 37)( 59, 94)( 60, 95)( 61, 96)
( 62, 97)( 63, 98)( 64, 99)( 65,100)( 66, 87)( 67, 88)( 68, 89)( 69, 90)
( 70, 91)( 71, 92)( 72, 93)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)
( 78, 85)( 79, 86)(108,143)(109,144)(110,145)(111,146)(112,147)(113,148)
(114,149)(115,136)(116,137)(117,138)(118,139)(119,140)(120,141)(121,142)
(122,129)(123,130)(124,131)(125,132)(126,133)(127,134)(128,135)(157,192)
(158,193)(159,194)(160,195)(161,196)(162,197)(163,198)(164,185)(165,186)
(166,187)(167,188)(168,189)(169,190)(170,191)(171,178)(172,179)(173,180)
(174,181)(175,182)(176,183)(177,184)(206,241)(207,242)(208,243)(209,244)
(210,245)(211,246)(212,247)(213,234)(214,235)(215,236)(216,237)(217,238)
(218,239)(219,240)(220,227)(221,228)(222,229)(223,230)(224,231)(225,232)
(226,233);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*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(247)!(1,2);
s1 := Sym(247)!(  4,  9)(  5,  8)(  6,  7)( 10, 45)( 11, 51)( 12, 50)( 13, 49)
( 14, 48)( 15, 47)( 16, 46)( 17, 38)( 18, 44)( 19, 43)( 20, 42)( 21, 41)
( 22, 40)( 23, 39)( 24, 31)( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 52,199)( 53,205)( 54,204)( 55,203)( 56,202)( 57,201)( 58,200)
( 59,241)( 60,247)( 61,246)( 62,245)( 63,244)( 64,243)( 65,242)( 66,234)
( 67,240)( 68,239)( 69,238)( 70,237)( 71,236)( 72,235)( 73,227)( 74,233)
( 75,232)( 76,231)( 77,230)( 78,229)( 79,228)( 80,220)( 81,226)( 82,225)
( 83,224)( 84,223)( 85,222)( 86,221)( 87,213)( 88,219)( 89,218)( 90,217)
( 91,216)( 92,215)( 93,214)( 94,206)( 95,212)( 96,211)( 97,210)( 98,209)
( 99,208)(100,207)(101,150)(102,156)(103,155)(104,154)(105,153)(106,152)
(107,151)(108,192)(109,198)(110,197)(111,196)(112,195)(113,194)(114,193)
(115,185)(116,191)(117,190)(118,189)(119,188)(120,187)(121,186)(122,178)
(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,171)(130,177)
(131,176)(132,175)(133,174)(134,173)(135,172)(136,164)(137,170)(138,169)
(139,168)(140,167)(141,166)(142,165)(143,157)(144,163)(145,162)(146,161)
(147,160)(148,159)(149,158);
s2 := Sym(247)!(  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)
( 10, 53)( 11, 52)( 12, 58)( 13, 57)( 14, 56)( 15, 55)( 16, 54)( 17, 95)
( 18, 94)( 19,100)( 20, 99)( 21, 98)( 22, 97)( 23, 96)( 24, 88)( 25, 87)
( 26, 93)( 27, 92)( 28, 91)( 29, 90)( 30, 89)( 31, 81)( 32, 80)( 33, 86)
( 34, 85)( 35, 84)( 36, 83)( 37, 82)( 38, 74)( 39, 73)( 40, 79)( 41, 78)
( 42, 77)( 43, 76)( 44, 75)( 45, 67)( 46, 66)( 47, 72)( 48, 71)( 49, 70)
( 50, 69)( 51, 68)(101,207)(102,206)(103,212)(104,211)(105,210)(106,209)
(107,208)(108,200)(109,199)(110,205)(111,204)(112,203)(113,202)(114,201)
(115,242)(116,241)(117,247)(118,246)(119,245)(120,244)(121,243)(122,235)
(123,234)(124,240)(125,239)(126,238)(127,237)(128,236)(129,228)(130,227)
(131,233)(132,232)(133,231)(134,230)(135,229)(136,221)(137,220)(138,226)
(139,225)(140,224)(141,223)(142,222)(143,214)(144,213)(145,219)(146,218)
(147,217)(148,216)(149,215)(150,158)(151,157)(152,163)(153,162)(154,161)
(155,160)(156,159)(164,193)(165,192)(166,198)(167,197)(168,196)(169,195)
(170,194)(171,186)(172,185)(173,191)(174,190)(175,189)(176,188)(177,187)
(178,179)(180,184)(181,183);
s3 := Sym(247)!( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 50)( 16, 51)
( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 43)( 23, 44)( 24, 31)
( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 29, 36)( 30, 37)( 59, 94)( 60, 95)
( 61, 96)( 62, 97)( 63, 98)( 64, 99)( 65,100)( 66, 87)( 67, 88)( 68, 89)
( 69, 90)( 70, 91)( 71, 92)( 72, 93)( 73, 80)( 74, 81)( 75, 82)( 76, 83)
( 77, 84)( 78, 85)( 79, 86)(108,143)(109,144)(110,145)(111,146)(112,147)
(113,148)(114,149)(115,136)(116,137)(117,138)(118,139)(119,140)(120,141)
(121,142)(122,129)(123,130)(124,131)(125,132)(126,133)(127,134)(128,135)
(157,192)(158,193)(159,194)(160,195)(161,196)(162,197)(163,198)(164,185)
(165,186)(166,187)(167,188)(168,189)(169,190)(170,191)(171,178)(172,179)
(173,180)(174,181)(175,182)(176,183)(177,184)(206,241)(207,242)(208,243)
(209,244)(210,245)(211,246)(212,247)(213,234)(214,235)(215,236)(216,237)
(217,238)(218,239)(219,240)(220,227)(221,228)(222,229)(223,230)(224,231)
(225,232)(226,233);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*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 >;

to this polytope