Multiply twinned particles with shapes beyond that of the complete icosahedron have been observed in island layers obtained by physical vapour deposition on alkali halide substrate. Image analysis applied to lattice plane images of one distinctive example of such particles by employing Fourier processing routines allowed to set up a detailed model of MTPs composed of two icosahedra stacked into each other. These icosahedra being in twin position share a central decahedron that does not exhibit external faces. So, the particle comprises 35 tetrahedral subunits, but has only 30 outer faces. Comparison of the image contrast calculated according to this model with the experimental electron microscopy image showed rather good agreement. The formation of such particles is assumed to proceed via successive growth twinning.