We are interested in how to use Projection Geometry to investigate and explain the properties of Reye’s configuration and regular dodecahedron projection about collinear and concurrent.

When we draw the straight line for every sides of their corresponding face of the regular polyhedron projection, they are perspective from a point if their corresponding vertices are joined by concurrent lines. We call the point of concurrence the perspective center.
We draw the straight lines for the diagonal line of their corresponding face of the polyhedron projection, and then we find that they are perspective from a line if the extensions of the corresponding sides and diagonal lines meet in collinear points. The line joining these points is called perspective axis.

[1] Hilbert D., Geometry and the Imagination, 1932(P94~143)

[2] Coxter, H.S.M. (Harold Scott Macdonald), Projective Geometry, Second Edition, Spring- Verlag, 1907 (P7~48)

[3] Fishback, W.T. (William Thompson), Projective and Euclidean Geometry, Second Edition, 1969(P32~69)

[4] Dorwart, Harold L.(Harold Laird) The Geometry of Incidence ,1966(P45~120)

[5] Cederberg, Judith N., A Course in Modern Geometries, Second Edition, 2001(P213~283)

[6]Wylie, Clarence Raymond, Introduction to Projection Geometry, 1970(P277~317)