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Polyhedra

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Kites or Squares?

In looking at the C4v diagram in the table, I see 1 square (purple base) 4 triangles (each adjacent to one side of the base) and 4 kites, filling out the figure. Yet the "faces" entry describes 4+1 squares. Why isn't that 1 Square + 4 kites? Thanks --Lbeaumont (talk) 00:05, 30 July 2013 (UTC)[reply]

Thanks for the catch, I corrected the table entries. I added another special case as a diminished cube with 3 square faces on top. Tom Ruen (talk) 00:45, 30 July 2013 (UTC)[reply]

Thanks for the update. I'm not clear on "Trigonal." Would it be correct to link it to: Trigonal or does it have a more general or more specific meaning in your usage? --Lbeaumont (talk) 11:32, 30 July 2013 (UTC)[reply]

What is so special?

I am not clear on:

The characteristic that distinguishes the special cases, differentiating these 3 from the ordinary cases, and
The characteristic, if any, that unifies this collection of 3 forms.

Thanks! --Lbeaumont (talk) 13:12, 30 July 2013 (UTC)[reply]

All 3 have the same topology - that's what unifies them. The 3 special cases simply have different geometries of interest. There is a continuum between them by a single parameter for a given dimension of triangles, or two parameters with varying shapes of isosceles triangles. Actually the tetrahedron can also be considered a limiting case as the kite faces degenerate into zero area. Tom Ruen (talk) 20:23, 30 July 2013 (UTC)[reply]

Pentagram

I saw the sentence "The three rhombic faces fold out flat to form three-fifths of a pentagram," which seemed to be talking about the Chestahedron from the diagram, so moved it. However, checking the reference to Frank Chester's site, the angles are actually about half a degree out from being sections of a pentagram. So either the sentence was just wrong, or it was actually talking about the third special case, in which case it should say "The three rhombic faces fold out flat to form half of a hexagram." I've now changed it to that. Especially Lime (talk) 12:38, 6 February 2015 (UTC)[reply]

Miscount with two of the Gyroelongated pyramid or (augmented antiprisms).

1. The image with the 9+1 triangles...is really just a total of 9 or 8+1.

Somebody must have counted a triangle "inside" the gyroelongated pyramid.

2. The Hexagonal Prism that claims to have 18 triangles & 1 hexagon is inaccurate. It's really suppose to be 24 triangles with a 2 full hexagonal base & top.

If I were to leave it at 18 triangles with the general construction it's suppose to have, it would not classify as a prism because it would not be a fully closed "solid" due to the lack of triangles to complete the structure.. There are 6 on top & 6 on bottom & 5 visible triangles on the side, which leaves only 1 triangle [out of the false set of 18] to fill in the gap of the entire hidden side which would actually require 7 addition triangles to the 5 visible side triangles, not merely 1 triangle where we cannot see.

True Premise (talk) 20:37, 21 April 2020 (UTC)[reply]