Icosatrihedron With 3 Regular Heptagons

3D Model

This is the same model as my Icosatrihedron with 3 Affine Heptagons except that the vertices have been “de-skewed” so that the 3 heptagons are now regular.

This can be seen by viewing any internal heptagon along the intersection of the other two. In the affine model they are mutually orthogonal and the projection (silhouette) from this angle is not equalateral.

In this version, the heptagons are no longer orthogonal, although the projection from this angle is now a regular heptagon.

The normal to any heptagon in this model is close to when intersection of all three heptagons is seen about half way between the center of a blue triangle and the vertex that it shares with a yellow triangle. From that angle, checking the lengths of the edges and diagonals will confirm that the heptagons are regular.

The de-skewing is based on the articles referenced in my Affine model, except that here they are applied in 3D whereas the article applies the de-skew to a single plane.