Placet
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Placet is a fictional planet that appeared in the Science Fictional story Placet is a Crazy Place by Fredric Brown.
It rotates in a figure eight pattern around two stars, Argyle I and Argyle II, moving faster than sound. It is the only planet that can eclipse itself twice at the same time, run into itself every 40 hours and chase itself out of sight.
This is made possible by the fact that Argyle I is normal matter and Argyle II is contraterrene or negative matter. Half way between them is a field where light is slowed down to the speed of sound. This field also affects the brains of human beings, resulting in extremely vivid visual hallucinations. Touch is unaffected.
This is complicated by the fact that the planet is composed of both ordinary and heavy matter. The core is made of this collapsed, heavy matter, giving the planet a gravity three quarters that of Earth. Animal life composed of this heavy matter lives on the core.