Polytope of Type {14,34}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,34}*952
Also Known As : {14,34|2}. if this polytope has another name.
Group : SmallGroup(952,38)
Rank : 3
Schlafli Type : {14,34}
Number of vertices, edges, etc : 14, 238, 34
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 :
{14,34,2} of size 1904
Vertex Figure Of :
{2,14,34} of size 1904
Quotients (Maximal Quotients in Boldface) :
7-fold quotients : {2,34}*136
14-fold quotients : {2,17}*68
17-fold quotients : {14,2}*56
34-fold quotients : {7,2}*28
119-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {28,34}*1904, {14,68}*1904
Permutation Representation (GAP) :
s0 := ( 18,103)( 19,104)( 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, 86)( 36, 87)( 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, 69)( 53, 70)( 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)(137,222)(138,223)(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)(154,205)(155,206)(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)(171,188)(172,189)(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);;
s1 := ( 1, 18)( 2, 34)( 3, 33)( 4, 32)( 5, 31)( 6, 30)( 7, 29)( 8, 28)
( 9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)
( 17, 19)( 35,103)( 36,119)( 37,118)( 38,117)( 39,116)( 40,115)( 41,114)
( 42,113)( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)( 48,107)( 49,106)
( 50,105)( 51,104)( 52, 86)( 53,102)( 54,101)( 55,100)( 56, 99)( 57, 98)
( 58, 97)( 59, 96)( 60, 95)( 61, 94)( 62, 93)( 63, 92)( 64, 91)( 65, 90)
( 66, 89)( 67, 88)( 68, 87)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)
( 75, 80)( 76, 79)( 77, 78)(120,137)(121,153)(122,152)(123,151)(124,150)
(125,149)(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)(132,142)
(133,141)(134,140)(135,139)(136,138)(154,222)(155,238)(156,237)(157,236)
(158,235)(159,234)(160,233)(161,232)(162,231)(163,230)(164,229)(165,228)
(166,227)(167,226)(168,225)(169,224)(170,223)(171,205)(172,221)(173,220)
(174,219)(175,218)(176,217)(177,216)(178,215)(179,214)(180,213)(181,212)
(182,211)(183,210)(184,209)(185,208)(186,207)(187,206)(189,204)(190,203)
(191,202)(192,201)(193,200)(194,199)(195,198)(196,197);;
s2 := ( 1,121)( 2,120)( 3,136)( 4,135)( 5,134)( 6,133)( 7,132)( 8,131)
( 9,130)( 10,129)( 11,128)( 12,127)( 13,126)( 14,125)( 15,124)( 16,123)
( 17,122)( 18,138)( 19,137)( 20,153)( 21,152)( 22,151)( 23,150)( 24,149)
( 25,148)( 26,147)( 27,146)( 28,145)( 29,144)( 30,143)( 31,142)( 32,141)
( 33,140)( 34,139)( 35,155)( 36,154)( 37,170)( 38,169)( 39,168)( 40,167)
( 41,166)( 42,165)( 43,164)( 44,163)( 45,162)( 46,161)( 47,160)( 48,159)
( 49,158)( 50,157)( 51,156)( 52,172)( 53,171)( 54,187)( 55,186)( 56,185)
( 57,184)( 58,183)( 59,182)( 60,181)( 61,180)( 62,179)( 63,178)( 64,177)
( 65,176)( 66,175)( 67,174)( 68,173)( 69,189)( 70,188)( 71,204)( 72,203)
( 73,202)( 74,201)( 75,200)( 76,199)( 77,198)( 78,197)( 79,196)( 80,195)
( 81,194)( 82,193)( 83,192)( 84,191)( 85,190)( 86,206)( 87,205)( 88,221)
( 89,220)( 90,219)( 91,218)( 92,217)( 93,216)( 94,215)( 95,214)( 96,213)
( 97,212)( 98,211)( 99,210)(100,209)(101,208)(102,207)(103,223)(104,222)
(105,238)(106,237)(107,236)(108,235)(109,234)(110,233)(111,232)(112,231)
(113,230)(114,229)(115,228)(116,227)(117,226)(118,225)(119,224);;
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,
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(238)!( 18,103)( 19,104)( 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, 86)( 36, 87)( 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, 69)( 53, 70)( 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)(137,222)(138,223)(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)(154,205)(155,206)(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)(171,188)(172,189)
(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);
s1 := Sym(238)!( 1, 18)( 2, 34)( 3, 33)( 4, 32)( 5, 31)( 6, 30)( 7, 29)
( 8, 28)( 9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 35,103)( 36,119)( 37,118)( 38,117)( 39,116)( 40,115)
( 41,114)( 42,113)( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)( 48,107)
( 49,106)( 50,105)( 51,104)( 52, 86)( 53,102)( 54,101)( 55,100)( 56, 99)
( 57, 98)( 58, 97)( 59, 96)( 60, 95)( 61, 94)( 62, 93)( 63, 92)( 64, 91)
( 65, 90)( 66, 89)( 67, 88)( 68, 87)( 70, 85)( 71, 84)( 72, 83)( 73, 82)
( 74, 81)( 75, 80)( 76, 79)( 77, 78)(120,137)(121,153)(122,152)(123,151)
(124,150)(125,149)(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)
(132,142)(133,141)(134,140)(135,139)(136,138)(154,222)(155,238)(156,237)
(157,236)(158,235)(159,234)(160,233)(161,232)(162,231)(163,230)(164,229)
(165,228)(166,227)(167,226)(168,225)(169,224)(170,223)(171,205)(172,221)
(173,220)(174,219)(175,218)(176,217)(177,216)(178,215)(179,214)(180,213)
(181,212)(182,211)(183,210)(184,209)(185,208)(186,207)(187,206)(189,204)
(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197);
s2 := Sym(238)!( 1,121)( 2,120)( 3,136)( 4,135)( 5,134)( 6,133)( 7,132)
( 8,131)( 9,130)( 10,129)( 11,128)( 12,127)( 13,126)( 14,125)( 15,124)
( 16,123)( 17,122)( 18,138)( 19,137)( 20,153)( 21,152)( 22,151)( 23,150)
( 24,149)( 25,148)( 26,147)( 27,146)( 28,145)( 29,144)( 30,143)( 31,142)
( 32,141)( 33,140)( 34,139)( 35,155)( 36,154)( 37,170)( 38,169)( 39,168)
( 40,167)( 41,166)( 42,165)( 43,164)( 44,163)( 45,162)( 46,161)( 47,160)
( 48,159)( 49,158)( 50,157)( 51,156)( 52,172)( 53,171)( 54,187)( 55,186)
( 56,185)( 57,184)( 58,183)( 59,182)( 60,181)( 61,180)( 62,179)( 63,178)
( 64,177)( 65,176)( 66,175)( 67,174)( 68,173)( 69,189)( 70,188)( 71,204)
( 72,203)( 73,202)( 74,201)( 75,200)( 76,199)( 77,198)( 78,197)( 79,196)
( 80,195)( 81,194)( 82,193)( 83,192)( 84,191)( 85,190)( 86,206)( 87,205)
( 88,221)( 89,220)( 90,219)( 91,218)( 92,217)( 93,216)( 94,215)( 95,214)
( 96,213)( 97,212)( 98,211)( 99,210)(100,209)(101,208)(102,207)(103,223)
(104,222)(105,238)(106,237)(107,236)(108,235)(109,234)(110,233)(111,232)
(112,231)(113,230)(114,229)(115,228)(116,227)(117,226)(118,225)(119,224);
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,
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 >;
References : None.
to this polytope