by wendy » Thu Oct 19, 2017 8:14 am
Think of these as their 3D versions.
A facet is something a jeweller cuts, is a different word to 'face', and is what you make when you 'facet' (spread bounding surfaces in) something. I use 'face' in the PG for this.
A ridge is the boundry between two faces or facets, is the line-shaped boundary that on a sphere, is higher than anywhere else (i use margin for this).
A peak is that the faces raise to a point at the second-margin in 3D.
In the PG, all words from /face/ refer to N-1 dimensions, so facing, facet, face, surface. The 2d element is a hedron (2d patch), part of a hedrix.
The word 'edge' in common use means a boundary of a closed space of indefinite space. So the edge of the galaxic state is shown as a 2d defence system, and the edge of the plate is the ring around the interior. I use latron for 1d line, and latrix (eg a piece of string or cotton), for the open 1d cloth (eg cotton on the spool).
Peak is still kept in the sense of raised thing, but it can acquire dimensionality. Appiculation is to raise peaks or pyramids on each face of a polytope. bi-apiculated is to raise peaks whose apexes are lines perpendicular to the margins they are above, and so forth.