Polytope of Type {38,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,6,3}*1368
if this polytope has a name.
Group : SmallGroup(1368,182)
Rank : 4
Schlafli Type : {38,6,3}
Number of vertices, edges, etc : 38, 114, 9, 3
Order of s₀s₁s₂s₃ : 114
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   3-fold quotients : {38,2,3}*456
   6-fold quotients : {19,2,3}*228
   19-fold quotients : {2,6,3}*72
   57-fold quotients : {2,2,3}*24
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);;
s1 := (  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)(  9, 13)
( 10, 12)( 20, 21)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)( 27, 33)
( 28, 32)( 29, 31)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)( 45, 53)
( 46, 52)( 47, 51)( 48, 50)( 58,116)( 59,115)( 60,133)( 61,132)( 62,131)
( 63,130)( 64,129)( 65,128)( 66,127)( 67,126)( 68,125)( 69,124)( 70,123)
( 71,122)( 72,121)( 73,120)( 74,119)( 75,118)( 76,117)( 77,135)( 78,134)
( 79,152)( 80,151)( 81,150)( 82,149)( 83,148)( 84,147)( 85,146)( 86,145)
( 87,144)( 88,143)( 89,142)( 90,141)( 91,140)( 92,139)( 93,138)( 94,137)
( 95,136)( 96,154)( 97,153)( 98,171)( 99,170)(100,169)(101,168)(102,167)
(103,166)(104,165)(105,164)(106,163)(107,162)(108,161)(109,160)(110,159)
(111,158)(112,157)(113,156)(114,155);;
s2 := (  1, 58)(  2, 59)(  3, 60)(  4, 61)(  5, 62)(  6, 63)(  7, 64)(  8, 65)
(  9, 66)( 10, 67)( 11, 68)( 12, 69)( 13, 70)( 14, 71)( 15, 72)( 16, 73)
( 17, 74)( 18, 75)( 19, 76)( 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, 77)( 40, 78)
( 41, 79)( 42, 80)( 43, 81)( 44, 82)( 45, 83)( 46, 84)( 47, 85)( 48, 86)
( 49, 87)( 50, 88)( 51, 89)( 52, 90)( 53, 91)( 54, 92)( 55, 93)( 56, 94)
( 57, 95)(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);;
s3 := (  1, 20)(  2, 21)(  3, 22)(  4, 23)(  5, 24)(  6, 25)(  7, 26)(  8, 27)
(  9, 28)( 10, 29)( 11, 30)( 12, 31)( 13, 32)( 14, 33)( 15, 34)( 16, 35)
( 17, 36)( 18, 37)( 19, 38)( 58,134)( 59,135)( 60,136)( 61,137)( 62,138)
( 63,139)( 64,140)( 65,141)( 66,142)( 67,143)( 68,144)( 69,145)( 70,146)
( 71,147)( 72,148)( 73,149)( 74,150)( 75,151)( 76,152)( 77,115)( 78,116)
( 79,117)( 80,118)( 81,119)( 82,120)( 83,121)( 84,122)( 85,123)( 86,124)
( 87,125)( 88,126)( 89,127)( 90,128)( 91,129)( 92,130)( 93,131)( 94,132)
( 95,133)( 96,153)( 97,154)( 98,155)( 99,156)(100,157)(101,158)(102,159)
(103,160)(104,161)(105,162)(106,163)(107,164)(108,165)(109,166)(110,167)
(111,168)(112,169)(113,170)(114,171);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*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(171)!(  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);
s1 := Sym(171)!(  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)
(  9, 13)( 10, 12)( 20, 21)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)
( 27, 33)( 28, 32)( 29, 31)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)
( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58,116)( 59,115)( 60,133)( 61,132)
( 62,131)( 63,130)( 64,129)( 65,128)( 66,127)( 67,126)( 68,125)( 69,124)
( 70,123)( 71,122)( 72,121)( 73,120)( 74,119)( 75,118)( 76,117)( 77,135)
( 78,134)( 79,152)( 80,151)( 81,150)( 82,149)( 83,148)( 84,147)( 85,146)
( 86,145)( 87,144)( 88,143)( 89,142)( 90,141)( 91,140)( 92,139)( 93,138)
( 94,137)( 95,136)( 96,154)( 97,153)( 98,171)( 99,170)(100,169)(101,168)
(102,167)(103,166)(104,165)(105,164)(106,163)(107,162)(108,161)(109,160)
(110,159)(111,158)(112,157)(113,156)(114,155);
s2 := Sym(171)!(  1, 58)(  2, 59)(  3, 60)(  4, 61)(  5, 62)(  6, 63)(  7, 64)
(  8, 65)(  9, 66)( 10, 67)( 11, 68)( 12, 69)( 13, 70)( 14, 71)( 15, 72)
( 16, 73)( 17, 74)( 18, 75)( 19, 76)( 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, 77)
( 40, 78)( 41, 79)( 42, 80)( 43, 81)( 44, 82)( 45, 83)( 46, 84)( 47, 85)
( 48, 86)( 49, 87)( 50, 88)( 51, 89)( 52, 90)( 53, 91)( 54, 92)( 55, 93)
( 56, 94)( 57, 95)(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);
s3 := Sym(171)!(  1, 20)(  2, 21)(  3, 22)(  4, 23)(  5, 24)(  6, 25)(  7, 26)
(  8, 27)(  9, 28)( 10, 29)( 11, 30)( 12, 31)( 13, 32)( 14, 33)( 15, 34)
( 16, 35)( 17, 36)( 18, 37)( 19, 38)( 58,134)( 59,135)( 60,136)( 61,137)
( 62,138)( 63,139)( 64,140)( 65,141)( 66,142)( 67,143)( 68,144)( 69,145)
( 70,146)( 71,147)( 72,148)( 73,149)( 74,150)( 75,151)( 76,152)( 77,115)
( 78,116)( 79,117)( 80,118)( 81,119)( 82,120)( 83,121)( 84,122)( 85,123)
( 86,124)( 87,125)( 88,126)( 89,127)( 90,128)( 91,129)( 92,130)( 93,131)
( 94,132)( 95,133)( 96,153)( 97,154)( 98,155)( 99,156)(100,157)(101,158)
(102,159)(103,160)(104,161)(105,162)(106,163)(107,164)(108,165)(109,166)
(110,167)(111,168)(112,169)(113,170)(114,171);
poly := sub<Sym(171)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*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