Packing and covering convex regions with congruent convex regions

Some thoughts that proceed from several earlier links, for example:
1. https://mathoverflow.net/questions/407397/least-area-and-least-perimeter-triangles-that-contain-a-convex-planar-region-h
2. https://mathoverflow.net/questions/352563/from-a-given-triangle-to-cut-2-mutually-congruent-convex-pieces-that-together
3. https://mathoverflow.net/questions/357124/on-comparing-planar-convex-regions-of-equal-perimeter-and-area
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Given a convex region C and an integer n, we are interested in finding
a. an optimal convex region C_a of maximum area such that n congruent copies of C_a can be put in the interior of C.
b. an optimal convex region C_p of maximum perimeter such that n congruent copies of C_p can be put in the interior of C.
c. an optimal convex region C_w of maximum least width such that n congruent copies of C_w can be put in the interior of C.

Question: Find the shapes of C such that {C_a, C_p, C_w} are pairwise maximally different.

Note 1: Consider C as a pentagon got by joining 2X1 rectangle to a long isosceles triangle of unit base attached to width of the rectangle. The C_w of this pentagon has width 1 and is a unit square. But a quadrilateral with width = 1/2 cut from the pentagon by the angular bisector of the isosceles apex is both its C_p and C_a. I can't think of any C where all C_p, C_a and C_w are wide apart or a C where C_p and C_w are same and C_a is rather different.

Note 2: If we try to find C_d - congruent pieces of maximum diameter - then, the answer could be degenerate.

Note 3: Instead of packing, we can consider **covering ** C with n congruent copies of some convex region such that this covering region has minimum area/perimeter/least width/diameter and compare the various optimal covering units.