Plato, _Tim._ 55 c 4. Neither this passage nor the last can refer to the Zodiac, which would be described by a dodecagon, not a dodecahedron. What is implied is the division of the heavens into twelve pentagonal fields. Footnote 810: Gow, _Short History of Greek Mathematics_, pp. 164 sqq. Footnote 811: This is pointed out by Kinkel, _Gesch. der Phil._ vol. i. p. 121. The tradition confirms in an interesting way the importance of the dodecahedron in the Pythagorean system. According to one account, Hippasos was drowned at sea for revealing its construction and claiming the discovery as his own.[812] What that construction was, we may partially infer from the fact that the Pythagoreans adopted the pentagram or _pentalpha_ as their symbol. The use of this figure in later magic is well known; and Paracelsus still employed it as a symbol of health, which is exactly what the Pythagoreans called it.[813] Footnote 812: Iambl. _V. Pyth._ 247. Cf. above, Chap. II. p. 117, _n._ 247. Footnote 813: See Gow, _Short History of Greek Mathematics_, p. 151, and the passages there referred to, adding Schol. Luc. p. 234, 21, Rabe, τὸ πεντάγραμμον] ὅτι τὸ ἐν τῇ συνθείᾳ λεγόμενον πένταλφα σύμβολον ἦν πρὸς ἀλλήλους Πυθαγορείων ἀναγνωριστικὸν καὶ τούτῳ ἐν ταῖς ἐπιστολαῖς ἐχρῶντο. [Sidenote: The Soul a “Harmony.”] 149. The view that the soul is a “harmony,” or rather an attunement, is intimately connected with the theory of the four elements. It cannot have belonged to the earliest form of Pythagoreanism; for, as shown in Plato’s _Phaedo_, it is quite inconsistent with the idea that the soul can exist independently of the body. It is the very opposite of the belief that “any soul can enter any body.”[814] On the other hand, we know also from the _Phaedo_ that it was accepted by Simmias and Kebes, who had heard Philolaos at Thebes, and by Echekrates of Phleious, who was the disciple of Philolaos and Eurytos.[815] The account of the doctrine given by Plato is quite in accordance with the view that it was of medical origin. Simmias says: “Our body being, as it were, strung and held together by the warm and the cold, the dry and the moist, and things of that sort, our soul is a sort of temperament and attunement of these, when they are mingled with one another well and in due proportion. If, then, our soul is an attunement, it is clear that, when the body has been relaxed or strung up out of measure by diseases and other ills, the soul must necessarily perish at once.”[816] This is clearly an application of the theory of Alkmaion (§ 96), and is in accordance with the views of the Sicilian school of medicine. It completes the evidence that the Pythagoreanism of the end of the fifth century was an adaptation of the old doctrine to the new principles introduced by Empedokles. Footnote 814: Arist. _de An._ Α, 3. 407 b 20 (R. P. 86 c). Footnote 815: Plato, _Phd._ 85 e sqq.; and for Echekrates, _ib._ 88 d. Footnote 816: