Polytope of Type {10,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,38}*760
Also Known As : {10,38|2}. if this polytope has another name.
Group : SmallGroup(760,35)
Rank : 3
Schlafli Type : {10,38}
Number of vertices, edges, etc : 10, 190, 38
Order of s₀s₁s₂ : 190
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,38,2} of size 1520
Vertex Figure Of :
   {2,10,38} of size 1520
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,38}*152
   10-fold quotients : {2,19}*76
   19-fold quotients : {10,2}*40
   38-fold quotients : {5,2}*20
   95-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,38}*1520, {10,76}*1520
Permutation Representation (GAP) :

s0 := ( 20, 77)( 21, 78)( 22, 79)( 23, 80)( 24, 81)( 25, 82)( 26, 83)( 27, 84)
( 28, 85)( 29, 86)( 30, 87)( 31, 88)( 32, 89)( 33, 90)( 34, 91)( 35, 92)
( 36, 93)( 37, 94)( 38, 95)( 39, 58)( 40, 59)( 41, 60)( 42, 61)( 43, 62)
( 44, 63)( 45, 64)( 46, 65)( 47, 66)( 48, 67)( 49, 68)( 50, 69)( 51, 70)
( 52, 71)( 53, 72)( 54, 73)( 55, 74)( 56, 75)( 57, 76)(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)(134,153)(135,154)(136,155)(137,156)(138,157)(139,158)(140,159)
(141,160)(142,161)(143,162)(144,163)(145,164)(146,165)(147,166)(148,167)
(149,168)(150,169)(151,170)(152,171);;
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, 77)( 40, 95)( 41, 94)( 42, 93)( 43, 92)
( 44, 91)( 45, 90)( 46, 89)( 47, 88)( 48, 87)( 49, 86)( 50, 85)( 51, 84)
( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 79)( 57, 78)( 59, 76)( 60, 75)
( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 96,115)
( 97,133)( 98,132)( 99,131)(100,130)(101,129)(102,128)(103,127)(104,126)
(105,125)(106,124)(107,123)(108,122)(109,121)(110,120)(111,119)(112,118)
(113,117)(114,116)(134,172)(135,190)(136,189)(137,188)(138,187)(139,186)
(140,185)(141,184)(142,183)(143,182)(144,181)(145,180)(146,179)(147,178)
(148,177)(149,176)(150,175)(151,174)(152,173)(154,171)(155,170)(156,169)
(157,168)(158,167)(159,166)(160,165)(161,164)(162,163);;
s2 := (  1, 97)(  2, 96)(  3,114)(  4,113)(  5,112)(  6,111)(  7,110)(  8,109)
(  9,108)( 10,107)( 11,106)( 12,105)( 13,104)( 14,103)( 15,102)( 16,101)
( 17,100)( 18, 99)( 19, 98)( 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)( 39,135)( 40,134)
( 41,152)( 42,151)( 43,150)( 44,149)( 45,148)( 46,147)( 47,146)( 48,145)
( 49,144)( 50,143)( 51,142)( 52,141)( 53,140)( 54,139)( 55,138)( 56,137)
( 57,136)( 58,154)( 59,153)( 60,171)( 61,170)( 62,169)( 63,168)( 64,167)
( 65,166)( 66,165)( 67,164)( 68,163)( 69,162)( 70,161)( 71,160)( 72,159)
( 73,158)( 74,157)( 75,156)( 76,155)( 77,173)( 78,172)( 79,190)( 80,189)
( 81,188)( 82,187)( 83,186)( 84,185)( 85,184)( 86,183)( 87,182)( 88,181)
( 89,180)( 90,179)( 91,178)( 92,177)( 93,176)( 94,175)( 95,174);;
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, 
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(190)!( 20, 77)( 21, 78)( 22, 79)( 23, 80)( 24, 81)( 25, 82)( 26, 83)
( 27, 84)( 28, 85)( 29, 86)( 30, 87)( 31, 88)( 32, 89)( 33, 90)( 34, 91)
( 35, 92)( 36, 93)( 37, 94)( 38, 95)( 39, 58)( 40, 59)( 41, 60)( 42, 61)
( 43, 62)( 44, 63)( 45, 64)( 46, 65)( 47, 66)( 48, 67)( 49, 68)( 50, 69)
( 51, 70)( 52, 71)( 53, 72)( 54, 73)( 55, 74)( 56, 75)( 57, 76)(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)(134,153)(135,154)(136,155)(137,156)(138,157)(139,158)
(140,159)(141,160)(142,161)(143,162)(144,163)(145,164)(146,165)(147,166)
(148,167)(149,168)(150,169)(151,170)(152,171);
s1 := Sym(190)!(  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, 77)( 40, 95)( 41, 94)( 42, 93)
( 43, 92)( 44, 91)( 45, 90)( 46, 89)( 47, 88)( 48, 87)( 49, 86)( 50, 85)
( 51, 84)( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 79)( 57, 78)( 59, 76)
( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)
( 96,115)( 97,133)( 98,132)( 99,131)(100,130)(101,129)(102,128)(103,127)
(104,126)(105,125)(106,124)(107,123)(108,122)(109,121)(110,120)(111,119)
(112,118)(113,117)(114,116)(134,172)(135,190)(136,189)(137,188)(138,187)
(139,186)(140,185)(141,184)(142,183)(143,182)(144,181)(145,180)(146,179)
(147,178)(148,177)(149,176)(150,175)(151,174)(152,173)(154,171)(155,170)
(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163);
s2 := Sym(190)!(  1, 97)(  2, 96)(  3,114)(  4,113)(  5,112)(  6,111)(  7,110)
(  8,109)(  9,108)( 10,107)( 11,106)( 12,105)( 13,104)( 14,103)( 15,102)
( 16,101)( 17,100)( 18, 99)( 19, 98)( 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)( 39,135)
( 40,134)( 41,152)( 42,151)( 43,150)( 44,149)( 45,148)( 46,147)( 47,146)
( 48,145)( 49,144)( 50,143)( 51,142)( 52,141)( 53,140)( 54,139)( 55,138)
( 56,137)( 57,136)( 58,154)( 59,153)( 60,171)( 61,170)( 62,169)( 63,168)
( 64,167)( 65,166)( 66,165)( 67,164)( 68,163)( 69,162)( 70,161)( 71,160)
( 72,159)( 73,158)( 74,157)( 75,156)( 76,155)( 77,173)( 78,172)( 79,190)
( 80,189)( 81,188)( 82,187)( 83,186)( 84,185)( 85,184)( 86,183)( 87,182)
( 88,181)( 89,180)( 90,179)( 91,178)( 92,177)( 93,176)( 94,175)( 95,174);
poly := sub<Sym(190)|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, 
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 : None.
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