I stumbled across this compound the other day, while playing around with Stella 4d: Polyhedron Navigator (available here).
At first, I thought this was a compound of six tetrahedra, but careful examination reveals that the tetrahedra are missing parts along the middle of some of their edges. I looked up the canonical compound of six tetrahedra in Stella‘s library, and here it is. As you can see, it’s quite similar — but it does have those “missing” pieces added.
RobertLovesPi.net 
You are so Smart!
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Not always, but I do try to be.
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I like it better this way than with the “Missing Parts”. Can you post the templates for the quadrilaterals and for the kites? I would like to build it.
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Here’s an image from the one with the missing pieces — I can’t easily get the other one. Just extend the edges of the central polygon to close up the gap, and this should work. https://robertlovespi.files.wordpress.com/2023/03/faces.png
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lovely!
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