Polytope of Type {38,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,10}*760
Also Known As : {38,10|2}. if this polytope has another name.
Group : SmallGroup(760,35)
Rank : 3
Schlafli Type : {38,10}
Number of vertices, edges, etc : 38, 190, 10
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 :
   {38,10,2} of size 1520
Vertex Figure Of :
   {2,38,10} of size 1520
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {38,2}*152
   10-fold quotients : {19,2}*76
   19-fold quotients : {2,10}*40
   38-fold quotients : {2,5}*20
   95-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {38,20}*1520, {76,10}*1520
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);;
s1 := (  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)(  9, 13)
( 10, 12)( 20, 78)( 21, 77)( 22, 95)( 23, 94)( 24, 93)( 25, 92)( 26, 91)
( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 86)( 32, 85)( 33, 84)( 34, 83)
( 35, 82)( 36, 81)( 37, 80)( 38, 79)( 39, 59)( 40, 58)( 41, 76)( 42, 75)
( 43, 74)( 44, 73)( 45, 72)( 46, 71)( 47, 70)( 48, 69)( 49, 68)( 50, 67)
( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)( 57, 60)( 96, 97)
( 98,114)( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)
(115,173)(116,172)(117,190)(118,189)(119,188)(120,187)(121,186)(122,185)
(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,178)(130,177)
(131,176)(132,175)(133,174)(134,154)(135,153)(136,171)(137,170)(138,169)
(139,168)(140,167)(141,166)(142,165)(143,164)(144,163)(145,162)(146,161)
(147,160)(148,159)(149,158)(150,157)(151,156)(152,155);;
s2 := (  1,115)(  2,116)(  3,117)(  4,118)(  5,119)(  6,120)(  7,121)(  8,122)
(  9,123)( 10,124)( 11,125)( 12,126)( 13,127)( 14,128)( 15,129)( 16,130)
( 17,131)( 18,132)( 19,133)( 20, 96)( 21, 97)( 22, 98)( 23, 99)( 24,100)
( 25,101)( 26,102)( 27,103)( 28,104)( 29,105)( 30,106)( 31,107)( 32,108)
( 33,109)( 34,110)( 35,111)( 36,112)( 37,113)( 38,114)( 39,172)( 40,173)
( 41,174)( 42,175)( 43,176)( 44,177)( 45,178)( 46,179)( 47,180)( 48,181)
( 49,182)( 50,183)( 51,184)( 52,185)( 53,186)( 54,187)( 55,188)( 56,189)
( 57,190)( 58,153)( 59,154)( 60,155)( 61,156)( 62,157)( 63,158)( 64,159)
( 65,160)( 66,161)( 67,162)( 68,163)( 69,164)( 70,165)( 71,166)( 72,167)
( 73,168)( 74,169)( 75,170)( 76,171)( 77,134)( 78,135)( 79,136)( 80,137)
( 81,138)( 82,139)( 83,140)( 84,141)( 85,142)( 86,143)( 87,144)( 88,145)
( 89,146)( 90,147)( 91,148)( 92,149)( 93,150)( 94,151)( 95,152);;
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, 
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(190)!(  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);
s1 := Sym(190)!(  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)
(  9, 13)( 10, 12)( 20, 78)( 21, 77)( 22, 95)( 23, 94)( 24, 93)( 25, 92)
( 26, 91)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 86)( 32, 85)( 33, 84)
( 34, 83)( 35, 82)( 36, 81)( 37, 80)( 38, 79)( 39, 59)( 40, 58)( 41, 76)
( 42, 75)( 43, 74)( 44, 73)( 45, 72)( 46, 71)( 47, 70)( 48, 69)( 49, 68)
( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)( 57, 60)
( 96, 97)( 98,114)( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)
(105,107)(115,173)(116,172)(117,190)(118,189)(119,188)(120,187)(121,186)
(122,185)(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,178)
(130,177)(131,176)(132,175)(133,174)(134,154)(135,153)(136,171)(137,170)
(138,169)(139,168)(140,167)(141,166)(142,165)(143,164)(144,163)(145,162)
(146,161)(147,160)(148,159)(149,158)(150,157)(151,156)(152,155);
s2 := Sym(190)!(  1,115)(  2,116)(  3,117)(  4,118)(  5,119)(  6,120)(  7,121)
(  8,122)(  9,123)( 10,124)( 11,125)( 12,126)( 13,127)( 14,128)( 15,129)
( 16,130)( 17,131)( 18,132)( 19,133)( 20, 96)( 21, 97)( 22, 98)( 23, 99)
( 24,100)( 25,101)( 26,102)( 27,103)( 28,104)( 29,105)( 30,106)( 31,107)
( 32,108)( 33,109)( 34,110)( 35,111)( 36,112)( 37,113)( 38,114)( 39,172)
( 40,173)( 41,174)( 42,175)( 43,176)( 44,177)( 45,178)( 46,179)( 47,180)
( 48,181)( 49,182)( 50,183)( 51,184)( 52,185)( 53,186)( 54,187)( 55,188)
( 56,189)( 57,190)( 58,153)( 59,154)( 60,155)( 61,156)( 62,157)( 63,158)
( 64,159)( 65,160)( 66,161)( 67,162)( 68,163)( 69,164)( 70,165)( 71,166)
( 72,167)( 73,168)( 74,169)( 75,170)( 76,171)( 77,134)( 78,135)( 79,136)
( 80,137)( 81,138)( 82,139)( 83,140)( 84,141)( 85,142)( 86,143)( 87,144)
( 88,145)( 89,146)( 90,147)( 91,148)( 92,149)( 93,150)( 94,151)( 95,152);
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, 
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.
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