Talk:Composite polyhedron

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Polyhedra

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	This article was accepted from this draft on 22 August 2024 by reviewer OnlyNano (talk · contribs).

enumeration

Zalgaller (1967) showed that there are twenty-eight non-composite polyhedra

Is this restricted to regular faces? Or perhaps there are 28 topologies that cannot be deformed into composites while retaining planar faces and convexity? —Tamfang (talk) 04:21, 18 November 2025 (UTC)

3 Platonic + 9 Archimedean + 17 Johnson = 29 —Antonissimo (talk) 04:21, 16 March 2026 (UTC)

Factual accuracy

There's currently some issue (at least) with the definitions.

The definition of composite in the lead paragraph does not match the definition section. Clearly any convex polyhedron can be sliced with a plane to produce two polyhedra. The restriction on edges is needed. Probably this was meant to be an informal description. But it reads like a precise statement and it's not really any more complex than the actual definition. No other definition of non-composite is offered than what is stated in the lead.
In the lead non-composite is required to have regular faces. Nowhere is composite required to. It's a little odd that these things seem like antonyms but are not. But then it states every composite polyhedron can be decomposed into non-composite polyhedra. Which is obviously false if non-composite is required to have regular faces. Even if both are required to have regular faces it is false as the bilunabirotunda can be cut along a cycle of edges to produce a non-regular hexagonal face. The only way to make sense of this fact is if non-composite is actually not required to have regular faces.
However then it states that multiple people have published papers discovering elementary polyhedra. These papers all seem to indicate something about regular faces in the title. This is also confusing because surely if they are required to have regular faces then they are a subset of the Johnson solids ∪ Archimedean solids, and their enumeration is easy, and it's given in the last paragraph (prisms, antiprisms, and 17 of the Johnson solids). Maybe the restriction to convex polyhedra in the lead is incorrect?

There are definitely some errors here which make the article a confusing read. AquitaneHungerForce (talk) 14:35, 19 November 2025 (UTC)

The first citation (that most closely follows the definition) specifies that the faces should be regular; this almost certainly is correct, and both the body and introduction are wrong (in different ways). I have added this specification into the body. --JBL (talk) 17:44, 15 March 2026 (UTC)

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