Although appearing earlier in the mathematical literature, it was rediscovered and popularized by M. C. Escher, who used it in the central image of his 1948 woodcut Stars.

A fourth isohedral deltahedron with the same face planes, also a stellation of the compound of three octahedra, has the same combinatorial structure as the tetrakis hexahedron but with the cube faces dented inwards into intersecting pyramids rather than attaching the pyramids to the exterior of the cube.

[2] In the 15th-century manuscript De quinque corporibus regularibus by Piero della Francesca, della Francesca already includes a drawing of an octahedron circumscribed around a cube, with eight of the cube edges lying in the octahedron's eight faces.

[7] H. S. M. Coxeter, assuming that Escher rediscovered this shape independently, writes that "It is remarkable that Escher, without any knowledge of algebra or analytic geometry, was able to rediscover this highly symmetrical figure.

"[2] However, George W. Hart has documented that Escher was familiar with Brückner's work and used it as the basis for many of the stellated polyhedra and polyhedral compounds that he drew.

[8] Earlier in 1948, Escher had made a preliminary woodcut with a similar theme, Study for Stars, but instead of using the compound of three regular octahedra in the study he used a different but related shape, a stellated rhombic dodecahedron (sometimes called Escher's solid), which can be formed as a compound of three flattened octahedra.

[7] The compound of three octahedra re-entered the mathematical literature more properly with the work of Bakos & Johnson (1959), who observed its existence and provided coordinates for its vertices.