In a search for a best substitute for a Symmetric Informationally Complete measurement in a real (not complex) Quantum Mechanics
Symmetric Informationally Complete measurements (SICs) play a central role in QBism. While in the standard Quantum Mechanics based on complex numbers, SICs exist for any size of the Hilbert space, in real Quantum Mechanics, only some Hilbert sizes feature them, and surrogates for SIC are sought. The lowest dimension in which it happens is four. As a very modest contribution to this project[FOW22], we suggested the vertices of a so-called runcinated four-dimensional tetrahedron, a four-dimensional Arcimedean solid, as an unperfect avatar of the four-dimensional real SIC. Incidentally, these vertices turned out to be the normals to the mirrors of the reflection group of the four-dimensional tetrahedron.