Talk:Ideal polyhedron

Ideal polyhedron has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.
Review: September 3, 2020. (Reviewed version).

A fact from Ideal polyhedron appeared on Wikipedia's Main Page in the Did you know column on 5 October 2020 (check views). The text of the entry was as follows:

Did you know... that unlike their Euclidean equivalents, the ideal regular tetrahedron, octahedron, and dodecahedron can all tile hyperbolic space (pictured)?

A record of the entry may be seen at Wikipedia:Recent additions/2020/October. The nomination discussion and review may be seen at Template:Did you know nominations/Ideal polyhedron.

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Polyhedra

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Did you know? nomination

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by Cwmhiraeth (talk) 05:29, 28 September 2020 (UTC)[reply]

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Tiling of hyperbolic space by ideal octahedra

... that unlike their Euclidean equivalents, the ideal regular tetrahedron, octahedron, and dodecahedron can all tile hyperbolic space (pictured)? Source: "Visualizing Hyperbolic Honeycombs", free arXiv version: "The tiling of euclidean space by cubes, {4,3,4}, is the only regular euclidean honeycomb" (page 1). The three ideal tilings are the ones in the first three rows of the left column of table 7 (page 23), but a more easily recognized statement of the hook claim can be found in "Euclidean decompositions of noncompact hyperbolic manifolds" [1], p. 78: "Suppose we have a tesselation of H3 by regular ideal hyperbolic polyhedra (i.e. with vertices at infinity). This is possible with tetrahedra, cubes, octahedra, and dodecahedra, but not with icosahedra."

Reviewed: Hainer Hill

Improved to Good Article status by David Eppstein (talk). Self-nominated at 06:29, 4 September 2020 (UTC).[reply]

New GA of good quality (and impressively readable for such a complex subject); no citation, policy, or copyright issues. Hook is appropriate length and interesting. QPQ is done. Image is freely licensed, grabs the attention, and shows up well. Good to go. Pi.1415926535 (talk) 04:42, 8 September 2020 (UTC)[reply]