Polytope of Type {152}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {152}*304
Also Known As : 152-gon, {152}. if this polytope has another name.
Group : SmallGroup(304,6)
Rank : 2
Schlafli Type : {152}
Number of vertices, edges, etc : 152, 152
Order of s0s1 : 152
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{152,2} of size 608
{152,4} of size 1216
{152,4} of size 1216
{152,6} of size 1824
Vertex Figure Of :
{2,152} of size 608
{4,152} of size 1216
{4,152} of size 1216
{6,152} of size 1824
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {76}*152
4-fold quotients : {38}*76
8-fold quotients : {19}*38
19-fold quotients : {8}*16
38-fold quotients : {4}*8
76-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {304}*608
3-fold covers : {456}*912
4-fold covers : {608}*1216
5-fold covers : {760}*1520
6-fold covers : {912}*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)( 39, 58)( 40, 76)( 41, 75)( 42, 74)( 43, 73)( 44, 72)
( 45, 71)( 46, 70)( 47, 69)( 48, 68)( 49, 67)( 50, 66)( 51, 65)( 52, 64)
( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 77,115)( 78,133)( 79,132)
( 80,131)( 81,130)( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)
( 88,123)( 89,122)( 90,121)( 91,120)( 92,119)( 93,118)( 94,117)( 95,116)
( 96,134)( 97,152)( 98,151)( 99,150)(100,149)(101,148)(102,147)(103,146)
(104,145)(105,144)(106,143)(107,142)(108,141)(109,140)(110,139)(111,138)
(112,137)(113,136)(114,135);;
s1 := (  1, 78)(  2, 77)(  3, 95)(  4, 94)(  5, 93)(  6, 92)(  7, 91)(  8, 90)
(  9, 89)( 10, 88)( 11, 87)( 12, 86)( 13, 85)( 14, 84)( 15, 83)( 16, 82)
( 17, 81)( 18, 80)( 19, 79)( 20, 97)( 21, 96)( 22,114)( 23,113)( 24,112)
( 25,111)( 26,110)( 27,109)( 28,108)( 29,107)( 30,106)( 31,105)( 32,104)
( 33,103)( 34,102)( 35,101)( 36,100)( 37, 99)( 38, 98)( 39,135)( 40,134)
( 41,152)( 42,151)( 43,150)( 44,149)( 45,148)( 46,147)( 47,146)( 48,145)
( 49,144)( 50,143)( 51,142)( 52,141)( 53,140)( 54,139)( 55,138)( 56,137)
( 57,136)( 58,116)( 59,115)( 60,133)( 61,132)( 62,131)( 63,130)( 64,129)
( 65,128)( 66,127)( 67,126)( 68,125)( 69,124)( 70,123)( 71,122)( 72,121)
( 73,120)( 74,119)( 75,118)( 76,117);;
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*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)( 39, 58)( 40, 76)( 41, 75)( 42, 74)( 43, 73)
( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 68)( 49, 67)( 50, 66)( 51, 65)
( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 77,115)( 78,133)
( 79,132)( 80,131)( 81,130)( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)
( 87,124)( 88,123)( 89,122)( 90,121)( 91,120)( 92,119)( 93,118)( 94,117)
( 95,116)( 96,134)( 97,152)( 98,151)( 99,150)(100,149)(101,148)(102,147)
(103,146)(104,145)(105,144)(106,143)(107,142)(108,141)(109,140)(110,139)
(111,138)(112,137)(113,136)(114,135);
s1 := Sym(152)!(  1, 78)(  2, 77)(  3, 95)(  4, 94)(  5, 93)(  6, 92)(  7, 91)
(  8, 90)(  9, 89)( 10, 88)( 11, 87)( 12, 86)( 13, 85)( 14, 84)( 15, 83)
( 16, 82)( 17, 81)( 18, 80)( 19, 79)( 20, 97)( 21, 96)( 22,114)( 23,113)
( 24,112)( 25,111)( 26,110)( 27,109)( 28,108)( 29,107)( 30,106)( 31,105)
( 32,104)( 33,103)( 34,102)( 35,101)( 36,100)( 37, 99)( 38, 98)( 39,135)
( 40,134)( 41,152)( 42,151)( 43,150)( 44,149)( 45,148)( 46,147)( 47,146)
( 48,145)( 49,144)( 50,143)( 51,142)( 52,141)( 53,140)( 54,139)( 55,138)
( 56,137)( 57,136)( 58,116)( 59,115)( 60,133)( 61,132)( 62,131)( 63,130)
( 64,129)( 65,128)( 66,127)( 67,126)( 68,125)( 69,124)( 70,123)( 71,122)
( 72,121)( 73,120)( 74,119)( 75,118)( 76,117);
poly := sub<Sym(152)|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*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope