Polytope of Type {38,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,14}*1064
Also Known As : {38,14|2}. if this polytope has another name.
Group : SmallGroup(1064,31)
Rank : 3
Schlafli Type : {38,14}
Number of vertices, edges, etc : 38, 266, 14
Order of s₀s₁s₂ : 266
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {38,2}*152
   14-fold quotients : {19,2}*76
   19-fold quotients : {2,14}*56
   38-fold quotients : {2,7}*28
   133-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 45, 52)
( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)
( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)( 81, 92)
( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)( 99,112)
(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(116,133)(117,132)
(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(135,152)
(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)(143,144)
(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)
(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)(197,204)
(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)(215,224)
(216,223)(217,222)(218,221)(219,220)(230,247)(231,246)(232,245)(233,244)
(234,243)(235,242)(236,241)(237,240)(238,239)(249,266)(250,265)(251,264)
(252,263)(253,262)(254,261)(255,260)(256,259)(257,258);;
s1 := (  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)(  9, 13)
( 10, 12)( 20,116)( 21,115)( 22,133)( 23,132)( 24,131)( 25,130)( 26,129)
( 27,128)( 28,127)( 29,126)( 30,125)( 31,124)( 32,123)( 33,122)( 34,121)
( 35,120)( 36,119)( 37,118)( 38,117)( 39, 97)( 40, 96)( 41,114)( 42,113)
( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)( 48,107)( 49,106)( 50,105)
( 51,104)( 52,103)( 53,102)( 54,101)( 55,100)( 56, 99)( 57, 98)( 58, 78)
( 59, 77)( 60, 95)( 61, 94)( 62, 93)( 63, 92)( 64, 91)( 65, 90)( 66, 89)
( 67, 88)( 68, 87)( 69, 86)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)
( 75, 80)( 76, 79)(134,135)(136,152)(137,151)(138,150)(139,149)(140,148)
(141,147)(142,146)(143,145)(153,249)(154,248)(155,266)(156,265)(157,264)
(158,263)(159,262)(160,261)(161,260)(162,259)(163,258)(164,257)(165,256)
(166,255)(167,254)(168,253)(169,252)(170,251)(171,250)(172,230)(173,229)
(174,247)(175,246)(176,245)(177,244)(178,243)(179,242)(180,241)(181,240)
(182,239)(183,238)(184,237)(185,236)(186,235)(187,234)(188,233)(189,232)
(190,231)(191,211)(192,210)(193,228)(194,227)(195,226)(196,225)(197,224)
(198,223)(199,222)(200,221)(201,220)(202,219)(203,218)(204,217)(205,216)
(206,215)(207,214)(208,213)(209,212);;
s2 := (  1,153)(  2,154)(  3,155)(  4,156)(  5,157)(  6,158)(  7,159)(  8,160)
(  9,161)( 10,162)( 11,163)( 12,164)( 13,165)( 14,166)( 15,167)( 16,168)
( 17,169)( 18,170)( 19,171)( 20,134)( 21,135)( 22,136)( 23,137)( 24,138)
( 25,139)( 26,140)( 27,141)( 28,142)( 29,143)( 30,144)( 31,145)( 32,146)
( 33,147)( 34,148)( 35,149)( 36,150)( 37,151)( 38,152)( 39,248)( 40,249)
( 41,250)( 42,251)( 43,252)( 44,253)( 45,254)( 46,255)( 47,256)( 48,257)
( 49,258)( 50,259)( 51,260)( 52,261)( 53,262)( 54,263)( 55,264)( 56,265)
( 57,266)( 58,229)( 59,230)( 60,231)( 61,232)( 62,233)( 63,234)( 64,235)
( 65,236)( 66,237)( 67,238)( 68,239)( 69,240)( 70,241)( 71,242)( 72,243)
( 73,244)( 74,245)( 75,246)( 76,247)( 77,210)( 78,211)( 79,212)( 80,213)
( 81,214)( 82,215)( 83,216)( 84,217)( 85,218)( 86,219)( 87,220)( 88,221)
( 89,222)( 90,223)( 91,224)( 92,225)( 93,226)( 94,227)( 95,228)( 96,191)
( 97,192)( 98,193)( 99,194)(100,195)(101,196)(102,197)(103,198)(104,199)
(105,200)(106,201)(107,202)(108,203)(109,204)(110,205)(111,206)(112,207)
(113,208)(114,209)(115,172)(116,173)(117,174)(118,175)(119,176)(120,177)
(121,178)(122,179)(123,180)(124,181)(125,182)(126,183)(127,184)(128,185)
(129,186)(130,187)(131,188)(132,189)(133,190);;
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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(266)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)
( 27, 32)( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)
( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)
( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(116,133)
(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)
(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)
(143,144)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)
(161,164)(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)
(179,184)(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)
(197,204)(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)
(215,224)(216,223)(217,222)(218,221)(219,220)(230,247)(231,246)(232,245)
(233,244)(234,243)(235,242)(236,241)(237,240)(238,239)(249,266)(250,265)
(251,264)(252,263)(253,262)(254,261)(255,260)(256,259)(257,258);
s1 := Sym(266)!(  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)
(  9, 13)( 10, 12)( 20,116)( 21,115)( 22,133)( 23,132)( 24,131)( 25,130)
( 26,129)( 27,128)( 28,127)( 29,126)( 30,125)( 31,124)( 32,123)( 33,122)
( 34,121)( 35,120)( 36,119)( 37,118)( 38,117)( 39, 97)( 40, 96)( 41,114)
( 42,113)( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)( 48,107)( 49,106)
( 50,105)( 51,104)( 52,103)( 53,102)( 54,101)( 55,100)( 56, 99)( 57, 98)
( 58, 78)( 59, 77)( 60, 95)( 61, 94)( 62, 93)( 63, 92)( 64, 91)( 65, 90)
( 66, 89)( 67, 88)( 68, 87)( 69, 86)( 70, 85)( 71, 84)( 72, 83)( 73, 82)
( 74, 81)( 75, 80)( 76, 79)(134,135)(136,152)(137,151)(138,150)(139,149)
(140,148)(141,147)(142,146)(143,145)(153,249)(154,248)(155,266)(156,265)
(157,264)(158,263)(159,262)(160,261)(161,260)(162,259)(163,258)(164,257)
(165,256)(166,255)(167,254)(168,253)(169,252)(170,251)(171,250)(172,230)
(173,229)(174,247)(175,246)(176,245)(177,244)(178,243)(179,242)(180,241)
(181,240)(182,239)(183,238)(184,237)(185,236)(186,235)(187,234)(188,233)
(189,232)(190,231)(191,211)(192,210)(193,228)(194,227)(195,226)(196,225)
(197,224)(198,223)(199,222)(200,221)(201,220)(202,219)(203,218)(204,217)
(205,216)(206,215)(207,214)(208,213)(209,212);
s2 := Sym(266)!(  1,153)(  2,154)(  3,155)(  4,156)(  5,157)(  6,158)(  7,159)
(  8,160)(  9,161)( 10,162)( 11,163)( 12,164)( 13,165)( 14,166)( 15,167)
( 16,168)( 17,169)( 18,170)( 19,171)( 20,134)( 21,135)( 22,136)( 23,137)
( 24,138)( 25,139)( 26,140)( 27,141)( 28,142)( 29,143)( 30,144)( 31,145)
( 32,146)( 33,147)( 34,148)( 35,149)( 36,150)( 37,151)( 38,152)( 39,248)
( 40,249)( 41,250)( 42,251)( 43,252)( 44,253)( 45,254)( 46,255)( 47,256)
( 48,257)( 49,258)( 50,259)( 51,260)( 52,261)( 53,262)( 54,263)( 55,264)
( 56,265)( 57,266)( 58,229)( 59,230)( 60,231)( 61,232)( 62,233)( 63,234)
( 64,235)( 65,236)( 66,237)( 67,238)( 68,239)( 69,240)( 70,241)( 71,242)
( 72,243)( 73,244)( 74,245)( 75,246)( 76,247)( 77,210)( 78,211)( 79,212)
( 80,213)( 81,214)( 82,215)( 83,216)( 84,217)( 85,218)( 86,219)( 87,220)
( 88,221)( 89,222)( 90,223)( 91,224)( 92,225)( 93,226)( 94,227)( 95,228)
( 96,191)( 97,192)( 98,193)( 99,194)(100,195)(101,196)(102,197)(103,198)
(104,199)(105,200)(106,201)(107,202)(108,203)(109,204)(110,205)(111,206)
(112,207)(113,208)(114,209)(115,172)(116,173)(117,174)(118,175)(119,176)
(120,177)(121,178)(122,179)(123,180)(124,181)(125,182)(126,183)(127,184)
(128,185)(129,186)(130,187)(131,188)(132,189)(133,190);
poly := sub<Sym(266)|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*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope