Polytope of Type {8,38,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,38,2}*1216
if this polytope has a name.
Group : SmallGroup(1216,1317)
Rank : 4
Schlafli Type : {8,38,2}
Number of vertices, edges, etc : 8, 152, 38, 2
Order of s₀s₁s₂s₃ : 152
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) :
   2-fold quotients : {4,38,2}*608
   4-fold quotients : {2,38,2}*304
   8-fold quotients : {2,19,2}*152
   19-fold quotients : {8,2,2}*64
   38-fold quotients : {4,2,2}*32
   76-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 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)( 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)( 96,134)( 97,135)
( 98,136)( 99,137)(100,138)(101,139)(102,140)(103,141)(104,142)(105,143)
(106,144)(107,145)(108,146)(109,147)(110,148)(111,149)(112,150)(113,151)
(114,152);;
s1 := (  1, 77)(  2, 95)(  3, 94)(  4, 93)(  5, 92)(  6, 91)(  7, 90)(  8, 89)
(  9, 88)( 10, 87)( 11, 86)( 12, 85)( 13, 84)( 14, 83)( 15, 82)( 16, 81)
( 17, 80)( 18, 79)( 19, 78)( 20, 96)( 21,114)( 22,113)( 23,112)( 24,111)
( 25,110)( 26,109)( 27,108)( 28,107)( 29,106)( 30,105)( 31,104)( 32,103)
( 33,102)( 34,101)( 35,100)( 36, 99)( 37, 98)( 38, 97)( 39,134)( 40,152)
( 41,151)( 42,150)( 43,149)( 44,148)( 45,147)( 46,146)( 47,145)( 48,144)
( 49,143)( 50,142)( 51,141)( 52,140)( 53,139)( 54,138)( 55,137)( 56,136)
( 57,135)( 58,115)( 59,133)( 60,132)( 61,131)( 62,130)( 63,129)( 64,128)
( 65,127)( 66,126)( 67,125)( 68,124)( 69,123)( 70,122)( 71,121)( 72,120)
( 73,119)( 74,118)( 75,117)( 76,116);;
s2 := (  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, 59)( 60, 76)( 61, 75)( 62, 74)( 63, 73)
( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 77, 78)( 79, 95)( 80, 94)( 81, 93)
( 82, 92)( 83, 91)( 84, 90)( 85, 89)( 86, 88)( 96, 97)( 98,114)( 99,113)
(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(115,116)(117,133)
(118,132)(119,131)(120,130)(121,129)(122,128)(123,127)(124,126)(134,135)
(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)(142,146)(143,145);;
s3 := (153,154);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*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(154)!( 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)( 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)( 96,134)
( 97,135)( 98,136)( 99,137)(100,138)(101,139)(102,140)(103,141)(104,142)
(105,143)(106,144)(107,145)(108,146)(109,147)(110,148)(111,149)(112,150)
(113,151)(114,152);
s1 := Sym(154)!(  1, 77)(  2, 95)(  3, 94)(  4, 93)(  5, 92)(  6, 91)(  7, 90)
(  8, 89)(  9, 88)( 10, 87)( 11, 86)( 12, 85)( 13, 84)( 14, 83)( 15, 82)
( 16, 81)( 17, 80)( 18, 79)( 19, 78)( 20, 96)( 21,114)( 22,113)( 23,112)
( 24,111)( 25,110)( 26,109)( 27,108)( 28,107)( 29,106)( 30,105)( 31,104)
( 32,103)( 33,102)( 34,101)( 35,100)( 36, 99)( 37, 98)( 38, 97)( 39,134)
( 40,152)( 41,151)( 42,150)( 43,149)( 44,148)( 45,147)( 46,146)( 47,145)
( 48,144)( 49,143)( 50,142)( 51,141)( 52,140)( 53,139)( 54,138)( 55,137)
( 56,136)( 57,135)( 58,115)( 59,133)( 60,132)( 61,131)( 62,130)( 63,129)
( 64,128)( 65,127)( 66,126)( 67,125)( 68,124)( 69,123)( 70,122)( 71,121)
( 72,120)( 73,119)( 74,118)( 75,117)( 76,116);
s2 := Sym(154)!(  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, 59)( 60, 76)( 61, 75)( 62, 74)
( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 77, 78)( 79, 95)( 80, 94)
( 81, 93)( 82, 92)( 83, 91)( 84, 90)( 85, 89)( 86, 88)( 96, 97)( 98,114)
( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(115,116)
(117,133)(118,132)(119,131)(120,130)(121,129)(122,128)(123,127)(124,126)
(134,135)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)(142,146)
(143,145);
s3 := Sym(154)!(153,154);
poly := sub<Sym(154)|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, s0*s1*s2*s1*s0*s1*s2*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 >;

to this polytope