We propose a microphone and loudspeaker array called the “tesseral array” that uses a tesseral crystal for spatial audio capture and synthesis. Because of the high symmetry of the array in terms of the position of microphones and loudspeakers, the rotation and reflection of the spatial sound field can be represented by simple matrix operations based on group theory without the encoding and decoding of spherical functions. We present a 26-channel array having 48 symmetry operations in which microphones and loudspeakers are positioned on the vertices of a cuboctahedron and its dual rhombic dodecahedron.
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