Single Comment

Ravioli Chess seems like a fundamentally interesting idea. A somewhat
similar family of CVs can be developed if we assume that:
(a) The playing field is one or more plane surfaces - folded, rolled or
layered onto itself.
(b) Specific, regularly placed pairs of locations on the playing field are
points of contact.
(c) Pieces occupying a point of contact may move from either their
physical or their virtual location (the location in the pair).
(d) Friendly units can virtually coexist but cannot physically occupy the
same location. Opposing units cannot coexist and moving to one location of
a location pair captures any opposing units on either location.
(e) Piece move along (or around) any plane region, provided that the path
from the starting location is open.

Some examples:

Toaster Pastry Chess:  The Q-side and K-side are notionally two layers,
with the edges of each side (perimeters a1-a8-d8-d1 and e1-e8-h8-h1) the
points of contact. Units on an edge of either half are also virtual
occupants of the space four spaces away, along the rank, in the other
half-board and may move within either half-board containing the physical
or the virtual starting space.

Pierogi (Calzone?) Chess:  The board is notionally rolled so that the a-
and h-files are aligned vertically, with the surface making contact along
the a-h files and each end rank. Units on the edge (a1-a8-h8-h1) may move
as in standard chess from either their physical location or from the
horizontal mirror image edge space.

Taco (Omelet?) Chess:  The board is notionally rolled as in Pierogi Chess,
but the contact is accomplished by the units -- each unit is effectively a
domino occupying both its physical location and its horizontal mirror
image (virtual) location. From either location, units move as in a
standard chess plane.

Turnover Chess:  The board is turned 45 degrees as in a diagonal form of
chess, and also notionally rolled so that the side corners (e.g., a8-h1)
align vertically. Pieces on the edge (a1-a8-h8-h1) move from their
physical location or from the (virtual) horizontal mirror image edge
location. Pawns are Berolina and a standard array might be adopted from
'Diagonal Chess' (L.A.Lewis) or 'Diamond Chess' (A.K. Porterfield
Rynd) -- see Pritchard's ECV. 

Of course, these CVs will not suit everyone's taste.
I will (wisely, I think) omit the details of possibilities such as
'Burrito Chess' or 'Cannoli Chess'.