Polytope of Type {14,38} with group SmallGroup(1064,31)

Overview

Group: SmallGroup(1064,31)
Rank: 3
Schläfli Type: {14,38}
Vertices, edges, …: 14, 266, 38
Order of s₀s₁s₂: 266
Order of s₀s₁s₂s₁: 2
Also known as: {14,38|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

7-fold

{2,38}*152

14-fold

{2,19}*76

19-fold

{14,2}*56

38-fold

{7,2}*28

133-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References