Cross-sections are computed by testing every tetrahedron of the shape against the cutting hyperplane (marching tetrahedra). Here that entire computation runs on the GPU: the 120-cell's 4,320 tetrahedra are classified in parallel each frame and the section triangles are written straight into the buffer the renderer draws — the geometry never touches the CPU.
The left and right shapes are the GPU and CPU computing the same cut; the readout above compares their triangle counts and areas live — they match to floating-point precision at every offset and rotation. Drag the slice through the whole shape and watch 720 dodecahedra stream past.