How to quickly cut a picture into hexagons?

Hello, how to cut any image into hexagons? ( I use Google translate )

For example, I downloaded a grid from Google at the request of Hexagons [weblink removed] , pasted it into Photoshop on top of the image on another layer, selected the grid with "Quick Selection", made an inversion on it, then I hid the mesh layer and switched to the image layer, pressed Delete and got the image "slicing", but the infection, there are several pixels of empty space between them, it's clear why.

How can I make this space white as small as possible, and ideally so that there would not even be a pixel of emptiness between the pieces of the puzzle, as if we are in the game assembling a puzzle from these pieces and when we have assembled everything correctly, no lines are visible, but only a solid image.

I'm probably ready to buy such an implementation, in the form of a template file and a video for 30 seconds, as all the settings were previously set in order to understand the process and so that I could cut a lot of images quickly, "like an onion in the kitchen"