Build solids with laminae?

Questions
,
1

Hello, from a beginner here. I want to build solids (cubes, tetrahedra, etc) using standard shape laminae (rectangles, triangles, circles, etc) or more complex objects such as a house of cards. I have looked at documentation under Lamina, LaminaData, etc, but cannot decipher how to do this. Any suggestion would be welcomed.

2

Type

Graphics3D[Table[Polygon[Join[#, {z}] & /@ Tuples[{0, 1}, 2]], {z, 0, 1, 1/7}]]

to start

comm856744.PNG
comm856744.PNG668×457 8.96 KB

create any graphics object, transform it systematically, collect them all in a list and display them with Graphics3D.

3

Thanks much for your input, Udo. It looks challenging and interesting. However, I need to start very simple. For example, just three planes, like building a house of cards. I need to know how to find the centroid and moment of inertia of such solid. Then later, more complex ones.

4

You should look at examples in documentation: Geometric Computation and specifically Region Properties and Measures - see Integral Measures there.

5

I need to know how to find the centroid and moment of inertia of such solid.

It tends to become numerical, so have a look at MeshCellCentroid, LaminaData, RegionCentroid, MomentOfInertia, RegionMoment and come up with more specific discussions …

6

Thanks for pointing me in the right direction, gentlemen.