Polytope of Type {38,8,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,8,2}*1216
if this polytope has a name.
Group : SmallGroup(1216,1317)
Rank : 4
Schlafli Type : {38,8,2}
Number of vertices, edges, etc : 38, 152, 8, 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 : {38,4,2}*608
4-fold quotients : {38,2,2}*304
8-fold quotients : {19,2,2}*152
19-fold quotients : {2,8,2}*64
38-fold quotients : {2,4,2}*32
76-fold quotients : {2,2,2}*16
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);;
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);;
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, 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(154)!( 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(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, 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(154)!( 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);
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,
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 >;
to this polytope