Polytope of Type {2,38,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,38,10}*1520
if this polytope has a name.
Group : SmallGroup(1520,174)
Rank : 4
Schlafli Type : {2,38,10}
Number of vertices, edges, etc : 2, 38, 190, 10
Order of s₀s₁s₂s₃ : 190
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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) :
   5-fold quotients : {2,38,2}*304
   10-fold quotients : {2,19,2}*152
   19-fold quotients : {2,2,10}*80
   38-fold quotients : {2,2,5}*40
   95-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)( 10, 15)( 11, 14)
( 12, 13)( 23, 40)( 24, 39)( 25, 38)( 26, 37)( 27, 36)( 28, 35)( 29, 34)
( 30, 33)( 31, 32)( 42, 59)( 43, 58)( 44, 57)( 45, 56)( 46, 55)( 47, 54)
( 48, 53)( 49, 52)( 50, 51)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)
( 66, 73)( 67, 72)( 68, 71)( 69, 70)( 80, 97)( 81, 96)( 82, 95)( 83, 94)
( 84, 93)( 85, 92)( 86, 91)( 87, 90)( 88, 89)( 99,116)(100,115)(101,114)
(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)(118,135)(119,134)
(120,133)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)(137,154)
(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)(145,146)
(156,173)(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)
(164,165)(175,192)(176,191)(177,190)(178,189)(179,188)(180,187)(181,186)
(182,185)(183,184);;
s2 := (  3,  4)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)( 10, 16)( 11, 15)
( 12, 14)( 22, 80)( 23, 79)( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28, 93)
( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 88)( 34, 87)( 35, 86)( 36, 85)
( 37, 84)( 38, 83)( 39, 82)( 40, 81)( 41, 61)( 42, 60)( 43, 78)( 44, 77)
( 45, 76)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 51, 70)( 52, 69)
( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)( 98, 99)
(100,116)(101,115)(102,114)(103,113)(104,112)(105,111)(106,110)(107,109)
(117,175)(118,174)(119,192)(120,191)(121,190)(122,189)(123,188)(124,187)
(125,186)(126,185)(127,184)(128,183)(129,182)(130,181)(131,180)(132,179)
(133,178)(134,177)(135,176)(136,156)(137,155)(138,173)(139,172)(140,171)
(141,170)(142,169)(143,168)(144,167)(145,166)(146,165)(147,164)(148,163)
(149,162)(150,161)(151,160)(152,159)(153,158)(154,157);;
s3 := (  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)( 20,134)( 21,135)( 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)( 39,115)( 40,116)( 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)( 58,191)
( 59,192)( 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)( 77,172)( 78,173)( 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)( 96,153)( 97,154);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(192)!(1,2);
s1 := Sym(192)!(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)( 10, 15)
( 11, 14)( 12, 13)( 23, 40)( 24, 39)( 25, 38)( 26, 37)( 27, 36)( 28, 35)
( 29, 34)( 30, 33)( 31, 32)( 42, 59)( 43, 58)( 44, 57)( 45, 56)( 46, 55)
( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 61, 78)( 62, 77)( 63, 76)( 64, 75)
( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 69, 70)( 80, 97)( 81, 96)( 82, 95)
( 83, 94)( 84, 93)( 85, 92)( 86, 91)( 87, 90)( 88, 89)( 99,116)(100,115)
(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)(118,135)
(119,134)(120,133)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)
(137,154)(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)
(145,146)(156,173)(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)
(163,166)(164,165)(175,192)(176,191)(177,190)(178,189)(179,188)(180,187)
(181,186)(182,185)(183,184);
s2 := Sym(192)!(  3,  4)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)( 10, 16)
( 11, 15)( 12, 14)( 22, 80)( 23, 79)( 24, 97)( 25, 96)( 26, 95)( 27, 94)
( 28, 93)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 88)( 34, 87)( 35, 86)
( 36, 85)( 37, 84)( 38, 83)( 39, 82)( 40, 81)( 41, 61)( 42, 60)( 43, 78)
( 44, 77)( 45, 76)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 51, 70)
( 52, 69)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 98, 99)(100,116)(101,115)(102,114)(103,113)(104,112)(105,111)(106,110)
(107,109)(117,175)(118,174)(119,192)(120,191)(121,190)(122,189)(123,188)
(124,187)(125,186)(126,185)(127,184)(128,183)(129,182)(130,181)(131,180)
(132,179)(133,178)(134,177)(135,176)(136,156)(137,155)(138,173)(139,172)
(140,171)(141,170)(142,169)(143,168)(144,167)(145,166)(146,165)(147,164)
(148,163)(149,162)(150,161)(151,160)(152,159)(153,158)(154,157);
s3 := Sym(192)!(  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)( 20,134)( 21,135)( 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)( 39,115)( 40,116)( 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)
( 58,191)( 59,192)( 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)( 77,172)( 78,173)( 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)( 96,153)( 97,154);
poly := sub<Sym(192)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >;

to this polytope