Polytope of Type {2,14,35}

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

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

Permutation Representation (Magma) :

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

to this polytope