Polytope of Type {2,14,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,34}*1904
if this polytope has a name.
Group : SmallGroup(1904,182)
Rank : 4
Schlafli Type : {2,14,34}
Number of vertices, edges, etc : 2, 14, 238, 34
Order of s₀s₁s₂s₃ : 238
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) :
   7-fold quotients : {2,2,34}*272
   14-fold quotients : {2,2,17}*136
   17-fold quotients : {2,14,2}*112
   34-fold quotients : {2,7,2}*56
   119-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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