How to use the hardware's 3D texture sampling with a flipbook style volume texture?

A question sort of addressing the problem and another question asking a related question.

I have a 2D texture that has 12x12 slices of a volume layered in a grid like this:

What I am doing now is to calculate the offset and sampling based of the 3D coordinate inside the volume using HLSL code myself. I have followed the descriptions found here and here, where the first link also talks about 3D sampling from a 2D sliced texture. I have also heard that modern hardware have the ability to sample 3D textures.

That being said, I have not found any description or example code that samples the 3D texture. What HLSL, or OpenGL, function can I use to sample this flipbook type of texture? If you can, please add a small example snippet with explanations. If you cant, pointing me to one or the documentation would be appreciated. I have found no sampler function where I can provide the number of layers in the U and V directions so I dont see how it can sample without knowing how many slices are per axis.

If I am misunderstanding this completely I would also appreciate being told so.

Thank you for your help.

OpenGL has support for true 3D textures for ages (actually 3D texture support already appeared in OpenGL-1.2). With that you upload your 3D texture not as a "flipbook" but simply as a stack of 2D images, using the function glTexImage3D. In GLSL you then just use the regular texture access function, but with a sampler3D and a 3 component texture coordinate vector (except in older versions of GLSL, i.e. before GLSL-1.5/OpenGL-3 where you use texture3D).