Pictures
Here are some pictures of the anticanonical surfaces inside some of our Fano 3-folds. In each case we express the Fano 
as a complete intersection in a toric variety 
, choose an affine chart on , take the intersection of an anticanonical hypersurface with that affine chart, and then take a generic projection of the resulting surface into affine 3-space. Thanks to Andrew MacPherson for the images.
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the rank-1 Fano 3-fold  |
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| The cubic 3-fold | |
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| Rank 3 #1 | |
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| Rank 3, #4 | |
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| Rank 4, #2 | |
Dudley Mallat
I found a great…