Polytope of Type {14,35,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,35,2}*1960
if this polytope has a name.
Group : SmallGroup(1960,137)
Rank : 4
Schlafli Type : {14,35,2}
Number of vertices, edges, etc : 14, 245, 35, 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 : {14,7,2}*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 := (  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);;
s1 := (  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 15, 43)
( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)( 23, 42)
( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)( 32, 33)
( 50,204)( 51,210)( 52,209)( 53,208)( 54,207)( 55,206)( 56,205)( 57,197)
( 58,203)( 59,202)( 60,201)( 61,200)( 62,199)( 63,198)( 64,239)( 65,245)
( 66,244)( 67,243)( 68,242)( 69,241)( 70,240)( 71,232)( 72,238)( 73,237)
( 74,236)( 75,235)( 76,234)( 77,233)( 78,225)( 79,231)( 80,230)( 81,229)
( 82,228)( 83,227)( 84,226)( 85,218)( 86,224)( 87,223)( 88,222)( 89,221)
( 90,220)( 91,219)( 92,211)( 93,217)( 94,216)( 95,215)( 96,214)( 97,213)
( 98,212)( 99,155)(100,161)(101,160)(102,159)(103,158)(104,157)(105,156)
(106,148)(107,154)(108,153)(109,152)(110,151)(111,150)(112,149)(113,190)
(114,196)(115,195)(116,194)(117,193)(118,192)(119,191)(120,183)(121,189)
(122,188)(123,187)(124,186)(125,185)(126,184)(127,176)(128,182)(129,181)
(130,180)(131,179)(132,178)(133,177)(134,169)(135,175)(136,174)(137,173)
(138,172)(139,171)(140,170)(141,162)(142,168)(143,167)(144,166)(145,165)
(146,164)(147,163);;
s2 := (  1, 51)(  2, 50)(  3, 56)(  4, 55)(  5, 54)(  6, 53)(  7, 52)(  8, 93)
(  9, 92)( 10, 98)( 11, 97)( 12, 96)( 13, 95)( 14, 94)( 15, 86)( 16, 85)
( 17, 91)( 18, 90)( 19, 89)( 20, 88)( 21, 87)( 22, 79)( 23, 78)( 24, 84)
( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 72)( 30, 71)( 31, 77)( 32, 76)
( 33, 75)( 34, 74)( 35, 73)( 36, 65)( 37, 64)( 38, 70)( 39, 69)( 40, 68)
( 41, 67)( 42, 66)( 43, 58)( 44, 57)( 45, 63)( 46, 62)( 47, 61)( 48, 60)
( 49, 59)( 99,198)(100,197)(101,203)(102,202)(103,201)(104,200)(105,199)
(106,240)(107,239)(108,245)(109,244)(110,243)(111,242)(112,241)(113,233)
(114,232)(115,238)(116,237)(117,236)(118,235)(119,234)(120,226)(121,225)
(122,231)(123,230)(124,229)(125,228)(126,227)(127,219)(128,218)(129,224)
(130,223)(131,222)(132,221)(133,220)(134,212)(135,211)(136,217)(137,216)
(138,215)(139,214)(140,213)(141,205)(142,204)(143,210)(144,209)(145,208)
(146,207)(147,206)(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);;
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*s0*s1*s2*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, 
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)!(  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);
s1 := Sym(247)!(  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)
( 15, 43)( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)
( 23, 42)( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)
( 32, 33)( 50,204)( 51,210)( 52,209)( 53,208)( 54,207)( 55,206)( 56,205)
( 57,197)( 58,203)( 59,202)( 60,201)( 61,200)( 62,199)( 63,198)( 64,239)
( 65,245)( 66,244)( 67,243)( 68,242)( 69,241)( 70,240)( 71,232)( 72,238)
( 73,237)( 74,236)( 75,235)( 76,234)( 77,233)( 78,225)( 79,231)( 80,230)
( 81,229)( 82,228)( 83,227)( 84,226)( 85,218)( 86,224)( 87,223)( 88,222)
( 89,221)( 90,220)( 91,219)( 92,211)( 93,217)( 94,216)( 95,215)( 96,214)
( 97,213)( 98,212)( 99,155)(100,161)(101,160)(102,159)(103,158)(104,157)
(105,156)(106,148)(107,154)(108,153)(109,152)(110,151)(111,150)(112,149)
(113,190)(114,196)(115,195)(116,194)(117,193)(118,192)(119,191)(120,183)
(121,189)(122,188)(123,187)(124,186)(125,185)(126,184)(127,176)(128,182)
(129,181)(130,180)(131,179)(132,178)(133,177)(134,169)(135,175)(136,174)
(137,173)(138,172)(139,171)(140,170)(141,162)(142,168)(143,167)(144,166)
(145,165)(146,164)(147,163);
s2 := Sym(247)!(  1, 51)(  2, 50)(  3, 56)(  4, 55)(  5, 54)(  6, 53)(  7, 52)
(  8, 93)(  9, 92)( 10, 98)( 11, 97)( 12, 96)( 13, 95)( 14, 94)( 15, 86)
( 16, 85)( 17, 91)( 18, 90)( 19, 89)( 20, 88)( 21, 87)( 22, 79)( 23, 78)
( 24, 84)( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 72)( 30, 71)( 31, 77)
( 32, 76)( 33, 75)( 34, 74)( 35, 73)( 36, 65)( 37, 64)( 38, 70)( 39, 69)
( 40, 68)( 41, 67)( 42, 66)( 43, 58)( 44, 57)( 45, 63)( 46, 62)( 47, 61)
( 48, 60)( 49, 59)( 99,198)(100,197)(101,203)(102,202)(103,201)(104,200)
(105,199)(106,240)(107,239)(108,245)(109,244)(110,243)(111,242)(112,241)
(113,233)(114,232)(115,238)(116,237)(117,236)(118,235)(119,234)(120,226)
(121,225)(122,231)(123,230)(124,229)(125,228)(126,227)(127,219)(128,218)
(129,224)(130,223)(131,222)(132,221)(133,220)(134,212)(135,211)(136,217)
(137,216)(138,215)(139,214)(140,213)(141,205)(142,204)(143,210)(144,209)
(145,208)(146,207)(147,206)(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);
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*s0*s1*s2*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, 
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