Number of segments on the surface of a gridded cuboid

Dear everyone,

I have a cuboid.

On the X axis, it's divided to 4 segments (i.e. by 3 lines parallel to z axis) (segx=4).

On the Y axis, it's divided to 3 segments (i.e. by 2 lines parallel to z axis) (segy=3).

On the Z axis, it's divided to 8 segments (i.e. by 7 lines parallel to x or y axes) (segz=8).

Each line between two grid points is called a segment. How many segments are there on the surface of this cube entirely? All the 6 sides are divided as I said (like Rubik's cube!).

The numbers I said were just an example. I need a formula based on segx and segy and segz for the number of segments on this cuboid.

I appreciate any help.

Thank you so much

Re: Number of segments on the surface of a gridded cuboid

Start by calculating the number of vertical segments.

The number of vertical columns is equal to the perimeter of the top: 2(x + y). That is 14 in the example.

Each vertical column consists of z segments (8 in this example). So, there are 8*14, or 112 vertical segments.

The general formula is 2z(x + y).

Similar formulas calculate the number of segments parallel to the X- and Y-axes.

The rest should be straightforward.

Re: Number of segments on the surface of a gridded cuboid

It seems like all you need to do to find the number of segments is to find the surface area. Take it to be the case that the side of a segment is of length 1. In your case the dimensions would be 3x4x8. The surface area is $\displaystyle 2(4\times 8)+2(3\times 8)+2(4\times 3)$