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MAX_MAP_BRUSHSIDES occurs when your map exceeds the VBSP 19 maximum defined brush amount.

The current limit is 65536, this is due to the VBSP 19 format using integers to allocate number of brushsides, and because 65536 is the largest possible number allowed in 16-bit computer architecture.

There is no fix for this without altering the BSP format and possibly breaking compatibility.

Perhaps in the future valve will release VBSP 20 with more allowable brushsides.

Hammer/Compiled brushsides discrepancy

The term "brush sides" is a bit misleading, if you've paid attention to your brush sides in hammer before, you may have noticed the compiled result was higher.

This is because when compiling, it includes the bounding box of a brush, which can be up to an additional 6 brushsides per brush. If a face is lined up with the edge of the bounding box(meaning not angled in any way) it will not add an additional brushside.

Example: A 5 sided pyramid shaped brush with the bottom face lining up the bottom of the bounding box. While the brush itself is only 5 sides, it will count as 10. The 5 extra brushsides come from the bounding box.

As rule of thumb for figuring this out easier. 6 + angled faces = brushsides per brush