Polytope of Type {148}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {148}*296
Also Known As : 148-gon, {148}. if this polytope has another name.
Group : SmallGroup(296,6)
Rank : 2
Schlafli Type : {148}
Number of vertices, edges, etc : 148, 148
Order of s0s1 : 148
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{148,2} of size 592
{148,4} of size 1184
{148,6} of size 1776
{148,6} of size 1776
Vertex Figure Of :
{2,148} of size 592
{4,148} of size 1184
{6,148} of size 1776
{6,148} of size 1776
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {74}*148
4-fold quotients : {37}*74
37-fold quotients : {4}*8
74-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {296}*592
3-fold covers : {444}*888
4-fold covers : {592}*1184
5-fold covers : {740}*1480
6-fold covers : {888}*1776
Permutation Representation (GAP) :
s0 := ( 2, 37)( 3, 36)( 4, 35)( 5, 34)( 6, 33)( 7, 32)( 8, 31)( 9, 30)
( 10, 29)( 11, 28)( 12, 27)( 13, 26)( 14, 25)( 15, 24)( 16, 23)( 17, 22)
( 18, 21)( 19, 20)( 39, 74)( 40, 73)( 41, 72)( 42, 71)( 43, 70)( 44, 69)
( 45, 68)( 46, 67)( 47, 66)( 48, 65)( 49, 64)( 50, 63)( 51, 62)( 52, 61)
( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 75,112)( 76,148)( 77,147)( 78,146)
( 79,145)( 80,144)( 81,143)( 82,142)( 83,141)( 84,140)( 85,139)( 86,138)
( 87,137)( 88,136)( 89,135)( 90,134)( 91,133)( 92,132)( 93,131)( 94,130)
( 95,129)( 96,128)( 97,127)( 98,126)( 99,125)(100,124)(101,123)(102,122)
(103,121)(104,120)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)
(111,113);;
s1 := ( 1, 76)( 2, 75)( 3,111)( 4,110)( 5,109)( 6,108)( 7,107)( 8,106)
( 9,105)( 10,104)( 11,103)( 12,102)( 13,101)( 14,100)( 15, 99)( 16, 98)
( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22, 92)( 23, 91)( 24, 90)
( 25, 89)( 26, 88)( 27, 87)( 28, 86)( 29, 85)( 30, 84)( 31, 83)( 32, 82)
( 33, 81)( 34, 80)( 35, 79)( 36, 78)( 37, 77)( 38,113)( 39,112)( 40,148)
( 41,147)( 42,146)( 43,145)( 44,144)( 45,143)( 46,142)( 47,141)( 48,140)
( 49,139)( 50,138)( 51,137)( 52,136)( 53,135)( 54,134)( 55,133)( 56,132)
( 57,131)( 58,130)( 59,129)( 60,128)( 61,127)( 62,126)( 63,125)( 64,124)
( 65,123)( 66,122)( 67,121)( 68,120)( 69,119)( 70,118)( 71,117)( 72,116)
( 73,115)( 74,114);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*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*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*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*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(148)!( 2, 37)( 3, 36)( 4, 35)( 5, 34)( 6, 33)( 7, 32)( 8, 31)
( 9, 30)( 10, 29)( 11, 28)( 12, 27)( 13, 26)( 14, 25)( 15, 24)( 16, 23)
( 17, 22)( 18, 21)( 19, 20)( 39, 74)( 40, 73)( 41, 72)( 42, 71)( 43, 70)
( 44, 69)( 45, 68)( 46, 67)( 47, 66)( 48, 65)( 49, 64)( 50, 63)( 51, 62)
( 52, 61)( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 75,112)( 76,148)( 77,147)
( 78,146)( 79,145)( 80,144)( 81,143)( 82,142)( 83,141)( 84,140)( 85,139)
( 86,138)( 87,137)( 88,136)( 89,135)( 90,134)( 91,133)( 92,132)( 93,131)
( 94,130)( 95,129)( 96,128)( 97,127)( 98,126)( 99,125)(100,124)(101,123)
(102,122)(103,121)(104,120)(105,119)(106,118)(107,117)(108,116)(109,115)
(110,114)(111,113);
s1 := Sym(148)!( 1, 76)( 2, 75)( 3,111)( 4,110)( 5,109)( 6,108)( 7,107)
( 8,106)( 9,105)( 10,104)( 11,103)( 12,102)( 13,101)( 14,100)( 15, 99)
( 16, 98)( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22, 92)( 23, 91)
( 24, 90)( 25, 89)( 26, 88)( 27, 87)( 28, 86)( 29, 85)( 30, 84)( 31, 83)
( 32, 82)( 33, 81)( 34, 80)( 35, 79)( 36, 78)( 37, 77)( 38,113)( 39,112)
( 40,148)( 41,147)( 42,146)( 43,145)( 44,144)( 45,143)( 46,142)( 47,141)
( 48,140)( 49,139)( 50,138)( 51,137)( 52,136)( 53,135)( 54,134)( 55,133)
( 56,132)( 57,131)( 58,130)( 59,129)( 60,128)( 61,127)( 62,126)( 63,125)
( 64,124)( 65,123)( 66,122)( 67,121)( 68,120)( 69,119)( 70,118)( 71,117)
( 72,116)( 73,115)( 74,114);
poly := sub<Sym(148)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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