I chose the Putnam Amphora because it pictures the three Greek deities who represent the three genres of the three sections of this book: Athena who stands in the center represents the section of Essays as the goddess of wisdom; after all she was born from the head of Zeus as is portrayed in the East pedimental sculptures of the Parthenon. To Athena's right (viewer’s left) stands Apollo who represents the section of Poems as the god of Music (which in Greece included poetry), and to her left stands Dionysus who represents the section of Stories as the god of drama.
The separate deities above (from the later red-figured pottery) are in the same position as those in the black-figured (early, generally 565-520 BC) vase on the cover of the book, though the deities are not portrayed in exactly the same stance, iconography, or mythical situation.
If you let the cursor rest on an image (either the small or the large image) a bit, the name of the deity will appear on it in white lettering. In the Dionysus scene Dionysus is on the right facing Herakles on the left; the heads that they are holding are probably that of Pentheus (Dionysus) and of Erginus perhaps (Herakles). However, the heads might possibly also be construed as actors' masks, since Dionysus was the god of drama.