This is a tough nut but not hard to crack so how about having a go and sending in your solution. This should help you to get started.
<p/>
There are 6 vertices and 5 edges. Let's suppose
the magic constant is 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>h</mi></mrow></math> and this is the same at
each vertex.  The total of all the numbers 1 + 2
+ ... + 11 = 66 but the numbers on the edges,

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>e</mi></mrow></math> are counted twice. So
<br />
<table width="100%"><tr><td align="center">
    <math xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo stretchy="false">)</mo><mo>+</mo><mn>66</mn><mo>=</mo><mn>6</mn><mi>h</mi><mo>.</mo></mrow>
    </mstyle></math>
</td></tr></table>
<br />

<p/>
So 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>e</mi></mrow></math> is a multiple of 6 and it is at
least 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>+</mo><mn>5</mn><mo>=</mo><mn>15</mn></mrow></math> so it must be 18 or more.
Hence 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mn>6</mn><mi>h</mi><mo>&#x2267;</mo><mn>84</mn></mrow></math> and 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>h</mi><mo>&#x2267;</mo><mn>14</mn></mrow></math>.
<p/>
Now you need to consider several cases for different values of 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>h</mi></mrow></math>, starting with 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>h</mi><mo>=</mo><mn>14</mn></mrow></math>, and for each value of 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>h</mi></mrow></math> you have information about the sum of the numbers on the five edges. Also for the feet you have to find 4 pairs of numbers adding up to 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>h</mi></mrow></math>.

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