Visualize 3D domain

There are a bunch of options to visualize Volumetric (4D) data, as in here.

What I am interested, however, is to visualize the 3D domain.

Now, the code itself is not the actual implementation, but it makes easier to explain. Say I want to visualize a 3D domain (like a 3D mesh) in polar coordinates.

The 3 spatial coordinates are , and the z coordinate changes as a function of the other variables, ie, .

clc; clear; close all force;

r = 1:0.2:2; % r coordinate discretization, from ri=1 to ro=2
theta = 0:pi/32:pi/4; % theta coordinate discretization, from theta_i = 0 to theta_o = pi/4
z = 0:0.2:1; % z coordinate discretization, from 0 to z_max, z_max = z(r,theta)
[R,Theta,Z] = ndgrid(r,theta,z);

figure; hold on;
for n=1:size(Z,3)
    z_max = 1+Theta(:,:,1)/theta(end);
    Z(:,:,n) = z(n)*z_max;
    mesh(R(:,:,n),Theta(:,:,n),Z(:,:,n),'FaceAlpha',0.5,'edgecolor',[0.5 0.5 0.5])
end
xlabel('r')
ylabel('\theta')
zlabel('z')
view(3)

Now, the code above produces the following figure:

This is almost what I want, but not exactly what I want. It sure helps to visualize the 3D domain, but I would like to also add the edge lines in the z direction, to create 3D cube-like shapes

Each vertex of the above grids is a vertex for a cube. Maybe a for loop could help to create this 3D mesh domain, but I don't know how.

Notice this is not the function itself I want to plot. Say, I have a dependent variable , so I could use the methods described in volume visualizations to visualize 4D data. What I want to plot is the 3D mesh that are the spatial variables and the domain of ϕ.

Is the multifaceted patch a solution to the problem or is there a better solution to it?