Polytope of Type {2,38,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,38,8}*1216
if this polytope has a name.
Group : SmallGroup(1216,1317)
Rank : 4
Schlafli Type : {2,38,8}
Number of vertices, edges, etc : 2, 38, 152, 8
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 : {2,38,4}*608
4-fold quotients : {2,38,2}*304
8-fold quotients : {2,19,2}*152
19-fold quotients : {2,2,8}*64
38-fold quotients : {2,2,4}*32
76-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);;
s2 := ( 3, 4)( 5, 21)( 6, 20)( 7, 19)( 8, 18)( 9, 17)( 10, 16)( 11, 15)
( 12, 14)( 22, 23)( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)
( 30, 34)( 31, 33)( 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)( 79,118)( 80,117)( 81,135)
( 82,134)( 83,133)( 84,132)( 85,131)( 86,130)( 87,129)( 88,128)( 89,127)
( 90,126)( 91,125)( 92,124)( 93,123)( 94,122)( 95,121)( 96,120)( 97,119)
( 98,137)( 99,136)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)
(106,148)(107,147)(108,146)(109,145)(110,144)(111,143)(112,142)(113,141)
(114,140)(115,139)(116,138);;
s3 := ( 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)( 39,115)( 40,116)( 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)( 58,153)
( 59,154)( 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)( 77,134)( 78,135);;
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,
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)!(1,2);
s1 := Sym(154)!( 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);
s2 := Sym(154)!( 3, 4)( 5, 21)( 6, 20)( 7, 19)( 8, 18)( 9, 17)( 10, 16)
( 11, 15)( 12, 14)( 22, 23)( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)
( 29, 35)( 30, 34)( 31, 33)( 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)( 79,118)( 80,117)
( 81,135)( 82,134)( 83,133)( 84,132)( 85,131)( 86,130)( 87,129)( 88,128)
( 89,127)( 90,126)( 91,125)( 92,124)( 93,123)( 94,122)( 95,121)( 96,120)
( 97,119)( 98,137)( 99,136)(100,154)(101,153)(102,152)(103,151)(104,150)
(105,149)(106,148)(107,147)(108,146)(109,145)(110,144)(111,143)(112,142)
(113,141)(114,140)(115,139)(116,138);
s3 := Sym(154)!( 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)( 39,115)( 40,116)( 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)
( 58,153)( 59,154)( 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)( 77,134)( 78,135);
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*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,
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