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Description
Start with an octahedron (red edges), add a zigzag path (green) that traces all edges once, and make a spline curve (yellow tube) crawl along the zigzag. What you get is what you see! The yellow worm's head (blue) makes two circuits while its tail (red) makes only one, before they meet and the worm vanishes! (Made in Mathematica and exported as a GIF, not a JIF.)

Description
Start with an octahedron (red edges), add a zigzag path (green) that traces all edges once, and make a spline curve (yellow tube) crawl along the zigzag. What you get is what you see! The yellow worm's head (blue) makes two circuits while its tail (red) makes only one, before they meet and the worm vanishes! (Made in Mathematica and exported as a GIF, not a JIF.)