Skew compound of four triangles (tetrahedral symmetry)

The skew compound of four triangles with tetrahedral symmetry is a regular skew compound of four planar triangles. It has a degree of freedom such that the components of the compound can vary in their distance from the center of the polygon.

Construction
It can be constructed by taking the faces of a tetrahedron and changing their distance from the circumcenter so that they no longer share edges or vertices.

It can also be constructed by taking half the faces of an octahedron and chaning their distance from the circumcenter.

Related polytopes
This compound is one of 4 regular skew compounds of triangles, counted by symmetry. There is a skew compound of four triangles with chiral cubic symmetry, along with two trival skew compounds of four triangles with hexagonal prismatic symmetry and hexagonal antiprismatic symmetry.

This compound is related to polyhedra compound of four trigonal dihedra. The compound of dihedra is regular in the sense of being flag-transitive if viewed as an embedding in $$\mathbb{R}^3$$ with flat faces even though the order of symmetry is only half of the number of flags, because multiple abstract isomorphisms correspond to the same spatial symmetry (for example, the two faces of one of the trigonal dihedra being swapped corresponds to the identity element of the spatial symmetry). However, it is not flag-transitive if viewed as a spherical tiling.