Acronym ...
Name 3/10-luna of hexacosachoron
  
 ©
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art 
                 o5o       
                        o5x
                           
            x5o            
     o5o                   
                        f5o
                 o5f       
                           
     o5x                   
            f5o            
                           
o5o                     x5x
                           
            o5f            
     x5o
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between peppy and tet:   arccos[-sqrt(5/8)] = 142.238756°
  • at {10} between pero and pero:   108°
  • at {5} between peppy and pero:   108°
  • at {3} between tet and pero:   arccos[(3-sqrt(5))/sqrt(32)] = 82.238756°
Face vector 53, 242, 353, 164
Confer
uniform relative:
ex  
related CRFs:
1/10-luna of ex   2/10-luna of ex   4/10-luna of ex   rotunda of ex  
general polytopal classes:
luna  

Incidence matrix

1 *  *  *  *  *  * ♦ 2 10  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 10 10 10  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 | 10 10  0  0 0  0  0  0  0  0  0  0  0  0 0  top
* 2  *  *  *  *  * ♦ 1  0  5  5  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |  5  0  0  5 10  5  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  5  0  5  5 1  0  0  0  0  0  0  0  0  0 0  pols of pseudo ike
* * 10  *  *  *  * ♦ 0  1  1  0  2  2  2  1  2  1  0  0  0  0  0  0  0  0  0 |  1  2  2  2  2  0  3  2  4  2  2  2  2  2  1  2  0  0  0  0  0  0 0  0  0  0 0 |  2  3  2  1 0  3  2  2  2  2  1  0  0  0 0  tropals of pseudo ike
* *  * 10  *  *  * ♦ 0  0  0  0  0  0  2  1  0  0  2  1  2  1  2  0  0  0  0 |  0  0  0  0  0  0  0  1  2  0  4  2  2  2  0  0  4  2  2  2  2  1 0  0  0  0 0 |  0  0  0  0 0  1  2  1  4  2  0  4  1  1 0  intermedials
* *  *  * 10  *  * | 0  0  0  1  0  0  0  0  2  0  0  1  0  0  0  2  2  0  0 |  0  0  0  0  2  2  0  0  0  1  0  2  0  0  2  2  0  0  2  0  0  0 1  2  1  0 0 |  0  0  1  2 1  0  0  1  0  2  2  0  1  0 1  top ones of peroes
* *  *  *  * 10  * | 0  0  0  0  0  0  0  0  0  1  0  0  2  1  0  0  2  2  0 |  0  0  0  0  0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  2  2  0 0  1  2  1 0 |  0  0  0  0 0  0  0  0  2  2  1  2  2  1 1  medial ones of peroes
* *  *  *  *  * 10 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  2  2 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  2  2  2 0  0  2  2 1 |  0  0  0  0 0  0  0  0  0  0  0  2  2  2 2  base ones of peroes (bottom)
-------------------+---------------------------------------------------------+--------------------------------------------------------------------------------+-------------------------------------------
1 1  0  0  0  0  0 | 2  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * |  5  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  5  0  0  0 0  0  0  0  0  0  0  0  0  0 0
1 0  1  0  0  0  0 | * 10  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * |  1  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  2  3  0  0 0  0  0  0  0  0  0  0  0  0 0
0 1  1  0  0  0  0 | *  * 10  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * |  1  0  0  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  2  0  2  1 0  0  0  0  0  0  0  0  0  0 0
0 1  0  0  1  0  0 | *  *  * 10  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * |  0  0  0  0  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  0  0  1  2 1  0  0  0  0  0  0  0  0  0 0
0 0  2  0  0  0  0 | *  *  *  * 10  *  *  *  *  *  *  *  *  *  *  *  *  *  * |  0  1  0  1  0  0  1  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  1  1  1  0 0  1  0  0  0  0  0  0  0  0 0  para
0 0  2  0  0  0  0 | *  *  *  *  * 10  *  *  *  *  *  *  *  *  *  *  *  *  * |  0  0  1  0  0  0  2  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  0  2  0  0 0  2  1  0  0  0  0  0  0  0 0  ortho
0 0  1  1  0  0  0 | *  *  *  *  *  * 20  *  *  *  *  *  *  *  *  *  *  *  * |  0  0  0  0  0  0  0  1  1  0  1  1  1  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  0  0  0  0 0  1  1  1  1  1  0  0  0  0 0  para
0 0  1  1  0  0  0 | *  *  *  *  *  *  * 10  *  *  *  *  *  *  *  *  *  *  * |  0  0  0  0  0  0  0  0  2  0  2  0  0  1  0  0  0  0  0  0  0  0 0  0  0  0 0 |  0  0  0  0 0  1  2  0  2  0  0  0  0  0 0  ortho
0 0  1  0  1  0  0 | *  *  *  *  *  *  *  * 20  *  *  *  *  *  *  *  *  *  * |  0  0  0  0  1  0  0  0  0  1  0  1  0  0  1  1  0  0  0  0  0  0 0  0  0  0 0 |  0  0  1  1 0  0  0  1  0  1  1  0  0  0 0
0 0  1  0  0  1  0 | *  *  *  *  *  *  *  *  * 10  *  *  *  *  *  *  *  *  * |  0  0  0  0  0  0  0  0  0  0  0  0  2  2  0  2  0  0  0  0  0  0 0  0  0  0 0 |  0  0  0  0 0  0  0  0  2  2  2  0  0  0 0
0 0  0  2  0  0  0 | *  *  *  *  *  *  *  *  *  * 10  *  *  *  *  *  *  *  * |  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  2  1  0  0  0  0 0  0  0  0 0 |  0  0  0  0 0  0  1  0  2  0  0  2  0  0 0
0 0  0  1  1  0  0 | *  *  *  *  *  *  *  *  *  *  * 10  *  *  *  *  *  *  * |  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0 0  0  0  0 0 |  0  0  0  0 0  0  0  1  0  2  0  0  1  0 0
0 0  0  1  0  1  0 | *  *  *  *  *  *  *  *  *  *  *  * 20  *  *  *  *  *  * |  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  1  0  1  1  0  0 0  0  0  0 0 |  0  0  0  0 0  0  0  0  1  1  0  1  1  0 0  para
0 0  0  1  0  1  0 | *  *  *  *  *  *  *  *  *  *  *  *  * 10  *  *  *  *  * |  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  2  0  0  0  2  0 0  0  0  0 0 |  0  0  0  0 0  0  0  0  2  0  0  2  0  1 0  ortho
0 0  0  1  0  0  1 | *  *  *  *  *  *  *  *  *  *  *  *  *  * 20  *  *  *  * |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1  1 0  0  0  0 0 |  0  0  0  0 0  0  0  0  0  0  0  2  1  1 0
0 0  0  0  2  0  0 | *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 10  *  *  * |  0  0  0  0  0  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0 1  1  0  0 0 |  0  0  0  1 1  0  0  0  0  0  1  0  0  0 1
0 0  0  0  1  1  0 | *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 20  *  * |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  1  0  0  0 0  1  1  0 0 |  0  0  0  0 0  0  0  0  0  1  1  0  1  0 1
0 0  0  0  0  1  1 | *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 20  * |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  0 0  0  1  1 0 |  0  0  0  0 0  0  0  0  0  0  0  1  1  1 1
0 0  0  0  0  0  2 | *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 10 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1 0  0  1  1 1 |  0  0  0  0 0  0  0  0  0  0  0  0  1  1 2
-------------------+---------------------------------------------------------+--------------------------------------------------------------------------------+-------------------------------------------
1 1  1  0  0  0  0 | 1  1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 10  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  2  0  0  0 0  0  0  0  0  0  0  0  0  0 0
1 0  2  0  0  0  0 | 0  2  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |  * 10  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  1  1  0  0 0  0  0  0  0  0  0  0  0  0 0
1 0  2  0  0  0  0 | 0  2  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0 |  *  * 10  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  0  2  0  0 0  0  0  0  0  0  0  0  0  0 0
0 1  2  0  0  0  0 | 0  0  2  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |  *  *  * 10  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  1  0  1  0 0  0  0  0  0  0  0  0  0  0 0
0 1  1  0  1  0  0 | 0  0  1  1  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0 |  *  *  *  * 20  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  0  0  1  1 0  0  0  0  0  0  0  0  0  0 0
0 1  0  0  2  0  0 | 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0 |  *  *  *  *  * 10  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  0  0  0  1 1  0  0  0  0  0  0  0  0  0 0
0 0  3  0  0  0  0 | 0  0  0  0  1  2  0  0  0  0  0  0  0  0  0  0  0  0  0 |  *  *  *  *  *  * 10  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  0  1  0  0 0  1  0  0  0  0  0  0  0  0 0
0 0  2  1  0  0  0 | 0  0  0  0  1  0  2  0  0  0  0  0  0  0  0  0  0  0  0 |  *  *  *  *  *  *  * 10  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  0  0  0  0 0  1  0  1  0  0  0  0  0  0 0  para
0 0  2  1  0  0  0 | 0  0  0  0  0  1  1  1  0  0  0  0  0  0  0  0  0  0  0 |  *  *  *  *  *  *  *  * 20  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  0  0  0  0 0  1  1  0  0  0  0  0  0  0 0  ortho
0 0  2  0  1  0  0 | 0  0  0  0  1  0  0  0  2  0  0  0  0  0  0  0  0  0  0 |  *  *  *  *  *  *  *  *  * 10  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  0  0  1  0 0  0  0  1  0  0  0  0  0  0 0
0 0  1  2  0  0  0 | 0  0  0  0  0  0  1  1  0  0  1  0  0  0  0  0  0  0  0 |  *  *  *  *  *  *  *  *  *  * 20  *  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  0  0  0  0 0  0  1  0  1  0  0  0  0  0 0
0 0  1  1  1  0  0 | 0  0  0  0  0  0  1  0  1  0  0  1  0  0  0  0  0  0  0 |  *  *  *  *  *  *  *  *  *  *  * 20  *  *  *  *  *  *  *  *  *  * *  *  *  * * |  0  0  0  0 0  0  0  1  0  1  0  0  0  0 0
0 0  1  1  0  1  0 | 0  0  0  0  0  0  1  0  0  1  0  0  1  0  0  0  0  0  0 |  *  *  *  *  *  *  *  *  *  *  *  * 20  *  *  *  *  *  *  *  *  * *  *  *  * * |  0  0  0  0 0  0  0  0  1  1  0  0  0  0 0  para
0 0  1  1  0  1  0 | 0  0  0  0  0  0  0  1  0  1  0  0  0  1  0  0  0  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  * 10  *  *  *  *  *  *  *  * *  *  *  * * |  0  0  0  0 0  0  0  0  2  0  0  0  0  0 0  ortho
0 0  1  0  2  0  0 | 0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  1  0  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  * 10  *  *  *  *  *  *  * *  *  *  * * |  0  0  0  1 0  0  0  0  0  0  1  0  0  0 0
0 0  1  0  1  1  0 | 0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0  1  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 20  *  *  *  *  *  * *  *  *  * * |  0  0  0  0 0  0  0  0  0  1  1  0  0  0 0
0 0  0  2  0  1  0 | 0  0  0  0  0  0  0  0  0  0  1  0  1  1  0  0  0  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 20  *  *  *  *  * *  *  *  * * |  0  0  0  0 0  0  0  0  1  0  0  1  0  0 0
0 0  0  2  0  0  1 | 0  0  0  0  0  0  0  0  0  0  1  0  0  0  2  0  0  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 10  *  *  *  * *  *  *  * * |  0  0  0  0 0  0  0  0  0  0  0  2  0  0 0
0 0  0  1  1  1  0 | 0  0  0  0  0  0  0  0  0  0  0  1  1  0  0  0  1  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 20  *  *  * *  *  *  * * |  0  0  0  0 0  0  0  0  0  1  0  0  1  0 0
0 0  0  1  0  1  1 | 0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  0  0  1  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 20  *  * *  *  *  * * |  0  0  0  0 0  0  0  0  0  0  0  1  1  0 0  para
0 0  0  1  0  1  1 | 0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0  1  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 20  * *  *  *  * * |  0  0  0  0 0  0  0  0  0  0  0  1  0  1 0  ortho
0 0  0  1  0  0  2 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  1 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 10 *  *  *  * * |  0  0  0  0 0  0  0  0  0  0  0  0  1  1 0
0 0  0  0  5  0  0 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  5  0  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 2  *  *  * * |  0  0  0  0 1  0  0  0  0  0  0  0  0  0 1
0 0  0  0  2  1  0 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  2  0  0 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * * 10  *  * * |  0  0  0  0 0  0  0  0  0  0  1  0  0  0 1
0 0  0  0  1  2  2 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  1 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  * 10  * * |  0  0  0  0 0  0  0  0  0  0  0  0  1  0 1
0 0  0  0  0  1  2 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  1 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  * 10 * |  0  0  0  0 0  0  0  0  0  0  0  0  0  1 1
0 0  0  0  0  0 10 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 10 |  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * *  *  *  * 1 |  0  0  0  0 0  0  0  0  0  0  0  0  0  0 2
-------------------+---------------------------------------------------------+--------------------------------------------------------------------------------+-------------------------------------------
1 1  2  0  0  0  0 | 1  2  2  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |  2  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 | 10  *  *  * *  *  *  *  *  *  *  *  *  * *  tet
1 0  3  0  0  0  0 | 0  3  0  0  1  2  0  0  0  0  0  0  0  0  0  0  0  0  0 |  0  1  2  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  * 10  *  * *  *  *  *  *  *  *  *  *  * *  tet
0 1  2  0  1  0  0 | 0  0  2  1  1  0  0  0  2  0  0  0  0  0  0  0  0  0  0 |  0  0  0  1  2  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  *  * 10  * *  *  *  *  *  *  *  *  *  * *  tet
0 1  1  0  2  0  0 | 0  0  1  2  0  0  0  0  2  0  0  0  0  0  0  1  0  0  0 |  0  0  0  0  2  1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0 0  0  0  0 0 |  *  *  * 10 *  *  *  *  *  *  *  *  *  * *  tet
0 1  0  0  5  0  0 | 0  0  0  5  0  0  0  0  0  0  0  0  0  0  0  5  0  0  0 |  0  0  0  0  0  5  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 1  0  0  0 0 |  *  *  *  * 2  *  *  *  *  *  *  *  *  * *  peppy
0 0  3  1  0  0  0 | 0  0  0  0  1  2  2  1  0  0  0  0  0  0  0  0  0  0  0 |  0  0  0  0  0  0  1  1  2  0  0  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  *  *  *  * * 10  *  *  *  *  *  *  *  * *  tet
0 0  2  2  0  0  0 | 0  0  0  0  0  1  2  2  0  0  1  0  0  0  0  0  0  0  0 |  0  0  0  0  0  0  0  0  2  0  2  0  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  *  *  *  * *  * 10  *  *  *  *  *  *  * *  tet
0 0  2  1  1  0  0 | 0  0  0  0  1  0  2  0  2  0  0  1  0  0  0  0  0  0  0 |  0  0  0  0  0  0  0  1  0  1  0  2  0  0  0  0  0  0  0  0  0  0 0  0  0  0 0 |  *  *  *  * *  *  * 10  *  *  *  *  *  * *  tet
0 0  1  2  0  1  0 | 0  0  0  0  0  0  1  1  0  1  1  0  1  1  0  0  0  0  0 |  0  0  0  0  0  0  0  0  0  0  1  0  1  1  0  0  1  0  0  0  0  0 0  0  0  0 0 |  *  *  *  * *  *  *  * 20  *  *  *  *  * *  tet
0 0  1  1  1  1  0 | 0  0  0  0  0  0  1  0  1  1  0  1  1  0  0  0  1  0  0 |  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0  1  0  0  1  0  0  0 0  0  0  0 0 |  *  *  *  * *  *  *  *  * 20  *  *  *  * *  tet
0 0  1  0  2  1  0 | 0  0  0  0  0  0  0  0  2  1  0  0  0  0  0  1  2  0  0 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  2  0  0  0  0  0  0 0  1  0  0 0 |  *  *  *  * *  *  *  *  *  * 10  *  *  * *  tet
0 0  0  2  0  1  1 | 0  0  0  0  0  0  0  0  0  0  1  0  1  1  2  0  0  1  0 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  1  1  0 0  0  0  0 0 |  *  *  *  * *  *  *  *  *  *  * 20  *  * *  tet
0 0  0  1  1  2  2 | 0  0  0  0  0  0  0  0  0  0  0  1  2  0  2  0  2  2  1 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  0  1 0  0  1  0 0 |  *  *  *  * *  *  *  *  *  *  *  * 10  * *  peppy
0 0  0  1  0  1  2 | 0  0  0  0  0  0  0  0  0  0  0  0  0  1  2  0  0  2  1 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  1 0  0  0  1 0 |  *  *  *  * *  *  *  *  *  *  *  *  * 10 *  tet
0 0  0  0  5  5 10 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  5 10 10 10 |  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 1  5  5  5 1 |  *  *  *  * *  *  *  *  *  *  *  *  *  * 2  pero

© 2004-2025
top of page