Polytope of Type {38,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,8}*608
Also Known As : {38,8|2}. if this polytope has another name.
Group : SmallGroup(608,105)
Rank : 3
Schlafli Type : {38,8}
Number of vertices, edges, etc : 38, 152, 8
Order of s₀s₁s₂ : 152
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {38,8,2} of size 1216
Vertex Figure Of :
   {2,38,8} of size 1216
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {38,4}*304
   4-fold quotients : {38,2}*152
   8-fold quotients : {19,2}*76
   19-fold quotients : {2,8}*32
   38-fold quotients : {2,4}*16
   76-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {76,8}*1216a, {38,16}*1216
   3-fold covers : {38,24}*1824, {114,8}*1824
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);;
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, 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)( 77,116)( 78,115)( 79,133)
( 80,132)( 81,131)( 82,130)( 83,129)( 84,128)( 85,127)( 86,126)( 87,125)
( 88,124)( 89,123)( 90,122)( 91,121)( 92,120)( 93,119)( 94,118)( 95,117)
( 96,135)( 97,134)( 98,152)( 99,151)(100,150)(101,149)(102,148)(103,147)
(104,146)(105,145)(106,144)(107,143)(108,142)(109,141)(110,140)(111,139)
(112,138)(113,137)(114,136);;
s2 := (  1, 77)(  2, 78)(  3, 79)(  4, 80)(  5, 81)(  6, 82)(  7, 83)(  8, 84)
(  9, 85)( 10, 86)( 11, 87)( 12, 88)( 13, 89)( 14, 90)( 15, 91)( 16, 92)
( 17, 93)( 18, 94)( 19, 95)( 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)( 39,134)( 40,135)
( 41,136)( 42,137)( 43,138)( 44,139)( 45,140)( 46,141)( 47,142)( 48,143)
( 49,144)( 50,145)( 51,146)( 52,147)( 53,148)( 54,149)( 55,150)( 56,151)
( 57,152)( 58,115)( 59,116)( 60,117)( 61,118)( 62,119)( 63,120)( 64,121)
( 65,122)( 66,123)( 67,124)( 68,125)( 69,126)( 70,127)( 71,128)( 72,129)
( 73,130)( 74,131)( 75,132)( 76,133);;
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, 
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(152)!(  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);
s1 := Sym(152)!(  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, 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)( 77,116)( 78,115)
( 79,133)( 80,132)( 81,131)( 82,130)( 83,129)( 84,128)( 85,127)( 86,126)
( 87,125)( 88,124)( 89,123)( 90,122)( 91,121)( 92,120)( 93,119)( 94,118)
( 95,117)( 96,135)( 97,134)( 98,152)( 99,151)(100,150)(101,149)(102,148)
(103,147)(104,146)(105,145)(106,144)(107,143)(108,142)(109,141)(110,140)
(111,139)(112,138)(113,137)(114,136);
s2 := Sym(152)!(  1, 77)(  2, 78)(  3, 79)(  4, 80)(  5, 81)(  6, 82)(  7, 83)
(  8, 84)(  9, 85)( 10, 86)( 11, 87)( 12, 88)( 13, 89)( 14, 90)( 15, 91)
( 16, 92)( 17, 93)( 18, 94)( 19, 95)( 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)( 39,134)
( 40,135)( 41,136)( 42,137)( 43,138)( 44,139)( 45,140)( 46,141)( 47,142)
( 48,143)( 49,144)( 50,145)( 51,146)( 52,147)( 53,148)( 54,149)( 55,150)
( 56,151)( 57,152)( 58,115)( 59,116)( 60,117)( 61,118)( 62,119)( 63,120)
( 64,121)( 65,122)( 66,123)( 67,124)( 68,125)( 69,126)( 70,127)( 71,128)
( 72,129)( 73,130)( 74,131)( 75,132)( 76,133);
poly := sub<Sym(152)|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, 
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