Polyhedra - Department of Mathematics

Figure 6.7. From an octahedron to a pentagonal dipyramid
Figure 6.8. From a pentagonal dipyramid to a snub disphenoid
Figure 6.9. From a snub disphenoid to a tri-augmented triangular prism
Figure 6.10. From a tri-augmented triangular prism to a gyro-elongated square dipyramid
However, we will encounter a problem when trying to carry out the same process on the
gyro-elongated square dipyramid. It is noted that no two consecutive edges or a "line"
connects the only two vertices of valency 4. These two vertices are joined by three edges.
By detaching these three edges, we obtained the icosahedra instead of a polyhedron with
eighteen faces.
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