Talk:Regular skew apeirohedron

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Infinite regular skew polyhedra in hyperbolic space

In process of checking this list below... Tom Ruen (talk) 21:08, 18 April 2013 (UTC)[reply]

infinite skew polyhedron says this, if I can find the source:

Beyond Euclidean 3-space, C. W. L. Garner determined a set of 32 regular skew polyhedra in hyperbolic 3-space, derived from the 4 regular hyperbolic honeycombs.

Garner, C. W. L. Regular Skew Polyhedra in Hyperbolic Three-Space. Canad. J. Math. 19, 1179-1186, 1967.

FOUND! [1]

SAME LIST, says 32, but it also enumerates 31 in the list, special case [(4,4,4,4)] → {8,8|4}, only has one form!

Coxeter vs McMullen

This article focuses on Coxeter's listing of 3 forms, while McMullen does his own in Abstract regular polytopes, accounting for 12. I moved a paragraph below from else where that needs to be better integrated here. Tom Ruen (talk) 11:30, 6 March 2015 (UTC)[reply]

According to McMullen, in full there are thirty regular apeirohedra in Euclidean space. These include the tessellations of type {4,4}, {6,3}, {3,6} above, as well as (in the plane) polytopes of type: {∞,3}, {∞,4}, {∞,6} and in 3-dimensional space, blends of these with either an apeirogon or a line segment, and the "pure" 3-dimensional apeirohedra (12 in number)

ref: McMullen & Schulte (2002, Section 7E)

Technical language

@2003 LN6: Hello. I was wondering if you could explain a bit what is objectionable about the language used in this article. Are there particular sections? Anything that could point in the direction of resolving the issue. AquitaneHungerForce (talk) 06:06, 4 February 2024 (UTC)[reply]

I would say that the history section is the hardest to read for normal readers and should be rewritten. 2003 LN6 (talk) 06:09, 4 February 2024 (UTC)[reply]

I rewrote that section. Let me know if you think it still needs anything. AquitaneHungerForce (talk) 07:57, 4 February 2024 (UTC)[reply]