user14767: Is it possible to create a "pawn box" as shown below (using legal moves and the help of black) in standard chess? 
The positions don't need to be exactly as shown, and there can be more pieces on the board if required.
[FEN "8/1k6/3PPP2/3P1P2/3PPP2/8/8/2K5 w - - 0 1"]

Note that this is, of course, not too difficult in horde chess as a black knight can remove the central pawn in the box.

user11629: This is really not difficult. Brian gave you one example, but you could imagine many more.
It is quite obvious that in order to achieve the "box" as given, white needs to capture 10 black pieces. 
Out of the 16 black pieces, all but the black king can help in achieving the box by letting themselves being captured.
The black a and h pawns don't seem at first all that useful as white wants to capture towards the center, however they could still help if they first capture white pieces then sacrificing themselves on say the b,c or  f,g files. 
A more interesting question could be: On which part of the board can you achieve such a box?

Trying to answer my own question (I label the box by its central square). 

box on h-file not possible because of border
box on g-file not possible (too many captures necessary)
box on f-file (I count 14 captures, so possible)
box on e-file possible, see example by Brian
files a-d don't need to be considered separately because of symmetry (a is the same as h, b the same as g, etc)

So in summary, it should be possible to create such box for white on the squares: c5, c6, d4, d5, d6, e4, e5, e6, f5, f6. Similarly for black on the mirrored squares: c3, c4, d3, d4, d5, e3, e4, e5, f3, f4.

user4418: Here is one simple solution:
[fen ""]

1.c4 d5 2.cxd5 e6 3.dxe6 f6 4.g4 g6 5.g5 Ne7 6.gxf6 Nd5 7.e4 Nc3 8.bxc3 Qd4 9.cxd4 b5 10.d5 b4 11.a3 c6 12.axb4 c5 13.bxc5 Bd6 14.cxd6 g5 15.h3 g4 16.hxg4 Rg8 17.f3 Rg5 18.f4 Rf5 19.gxf5 Na6 20.d4

More moves can be added to reach the exact position with no other pieces other than kings.

user15543: As @BrianTowers showed, it can be done. Here’s a shorter proof game for the fun of it.
[FEN ""]

1. h4 g5 2. hxg5 f5 3. g4 Nf6 4. gxf6 d6 5. gxf5 Be6 6. f4 Bb3 7. axb3 c5 8. e4 c4 9. bxc4 d5 10. cxd5 e6 11. dxe6 Na6 12. b4 Nc5 13. bxc5 Qd5 14. c4 Bd6 15. cxd6 Rf8 16. cxd5 Rh8 17. d4


14767: <p>Is it possible to create a "pawn box" as shown below (using legal moves and the help of black) in standard chess? </p>

<p>The positions don't need to be exactly as shown, and there can be more pieces on the board if required.</p>

<pre><code>[FEN "8/1k6/3PPP2/3P1P2/3PPP2/8/8/2K5 w - - 0 1"]
</code></pre>

<p>Note that this is, of course, not too difficult in <em>horde</em> chess as a black knight can remove the central pawn in the box.</p>
 11629: <p>This is really not difficult. Brian gave you one example, but you could imagine many more.</p>

<p>It is quite obvious that in order to achieve the "box" as given, white needs to capture 10 black pieces. </p>

<p>Out of the 16 black pieces, all but the black king can help in achieving the box by letting themselves being captured.</p>

<p>The black a and h pawns don't seem at first all that useful as white wants to capture towards the center, however they could still help if they first capture white pieces then sacrificing themselves on say the b,c or  f,g files. </p>

<p>A more interesting question could be: On which part of the board can you achieve such a box?</p>

<hr>

<p>Trying to answer my own question (I label the box by its central square). </p>

<ol>
<li>box on h-file not possible because of border</li>
<li>box on g-file not possible (too many captures necessary)</li>
<li>box on f-file (I count 14 captures, so possible)</li>
<li>box on e-file possible, see example by Brian</li>
<li>files a-d don't need to be considered separately because of symmetry (a is the same as h, b the same as g, etc)</li>
</ol>

<p>So in summary, it should be possible to create such box for white on the squares: c5, c6, d4, d5, d6, e4, e5, e6, f5, f6. Similarly for black on the mirrored squares: c3, c4, d3, d4, d5, e3, e4, e5, f3, f4.</p>
 4418: <p>Here is one simple solution:</p>

<pre><code>[fen ""]

1.c4 d5 2.cxd5 e6 3.dxe6 f6 4.g4 g6 5.g5 Ne7 6.gxf6 Nd5 7.e4 Nc3 8.bxc3 Qd4 9.cxd4 b5 10.d5 b4 11.a3 c6 12.axb4 c5 13.bxc5 Bd6 14.cxd6 g5 15.h3 g4 16.hxg4 Rg8 17.f3 Rg5 18.f4 Rf5 19.gxf5 Na6 20.d4
</code></pre>

<p>More moves can be added to reach the exact position with no other pieces other than kings.</p>
 15543: <p>As @BrianTowers showed, it can be done. Here’s a shorter proof game for the fun of it.</p>

<pre><code>[FEN ""]

1. h4 g5 2. hxg5 f5 3. g4 Nf6 4. gxf6 d6 5. gxf5 Be6 6. f4 Bb3 7. axb3 c5 8. e4 c4 9. bxc4 d5 10. cxd5 e6 11. dxe6 Na6 12. b4 Nc5 13. bxc5 Qd5 14. c4 Bd6 15. cxd6 Rf8 16. cxd5 Rh8 17. d4
</code></pre>
