Polytope of Type {34,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,14}*952
Also Known As : {34,14|2}. if this polytope has another name.
Group : SmallGroup(952,38)
Rank : 3
Schlafli Type : {34,14}
Number of vertices, edges, etc : 34, 238, 14
Order of s₀s₁s₂ : 238
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {34,14,2} of size 1904
Vertex Figure Of :
   {2,34,14} of size 1904
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {34,2}*136
   14-fold quotients : {17,2}*68
   17-fold quotients : {2,14}*56
   34-fold quotients : {2,7}*28
   119-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {34,28}*1904, {68,14}*1904
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope