The blurb on the cover of Hartmut Endlich’s book Das Pentagon-Dodekaeder als strukturgebendes Maß des Menschen [The pentagonal dodecahedron as a structural measure of the human being]1 promises a lot. Does it deliver? The visuals alone might make it worthwhile for those who don’t speak German.
The book begins with Leonardo da Vinci’s world-famous image of the human being standing in a square and a circle. The author, an anthroposophical physician, then goes on to discuss today’s fragmented natural science, “medicine and pharmacy based on fragments of knowledge,” in which “no path to healing in the sense of really becoming healthier” can be found. He presents his methodology as a macroscopic activity, which, following Goethe’s example, leads back to wholeness. This wholeness is found in geometry, in the Platonic solids. The pentagonal dodecahedron stands out among these due to certain characteristic features. By drawing lines connecting its various vertices, all the other Platonic solids can be found within it. This is unique among the Platonic solids. We marvel at Johannes Kepler’s drawings, where he assigns four of these solids to the four elements from Plato and represents them with the symbols of earth, water, air, and fire. The pentagonal dodecahedron, however, which contains all other Platonic solids within itself, is assigned to the quinta essentia [fifth essence], as the all-encompassing cosmos, and is marked with symbols of the heavens.
The author then introduces the golden ratio and its relationship to the pentagonal dodecahedron. This ratio, however, does not provide us with a holistic view of the proportions of the human body. Therefore, the author projects the pentagonal dodecahedron onto a plane, which leads to his discovery. By drawing pentagrams in the pentagonal surfaces of this projection, a pattern of lines emerges. When this is superimposed upon the human skeleton, a correspondence between the projected figure and the shape of the human body is revealed. This projection of the pentagon dodecahedron even relates to the chakras!
A vividly illustrated journey through anatomy follows, revealing further connections between humans and dodecahedrons. We see that the cosmic twelvefold nature of the pentagonal dodecahedron is more perfected in the human skeleton than in the animal. Then, we head back to geometry. By constructing an icosahedron around the pentagonal dodecahedron and then a dodecahedron around this, a spatial structure between point and infinity is created as the series is continued. Humans combine these spatial laws and proportions within themselves in a variety of ways and are thus connected to infinity and the spiritual world. In the foreword, the author expresses his hope that human beings should once again experience themselves as beings between heaven and earth, as an organization full of the wisdom of cosmic laws; the book makes this hope accessible and concrete. With this in consideration, it’s not surprising that Rudolf Steiner, together with the physician Felix Peipers, wanted to create pentagonal dodecahedrons as therapeutic color chambers and include them as part of the Johannesbau project in Munich.2 The first part of the book concludes with beautiful color designs of various projections of pentagonal dodecahedrons. The images address our soul directly, and we experience the aesthetic beauty of this miraculous image interwoven with the golden ratio.
The second part of the book contains detailed instructions for constructing the Platonic solids, illustrated with color photographs. There are also various techniques for constructing and stabilizing pentagonal dodecahedra using wooden rods. By stretching colored threads inside the spatial figure, the other Platonic solids can be created, as was known already by Plato.
The book is well-organized and beautifully designed, featuring numerous illustrations and photos. It provides an exemplar of Goetheanism. The author and inventor of the Cubus X3 appeals to the whole human being: our thinking and imagination by tracing the laws of the cosmos and our feeling life through artistic activities; and building the Platonic solids involves physical implementation with our hands. The main strength of the book is the fact that it encourages us to understand things through our own activity. It certainly lives up to the promise on its back cover! I recommend this book to anyone interested in medicine who would like to explore the human form in greater depth, but also to anyone ready to learn something new. Even if you usually avoid geometry, you will find the book easy to follow thanks to its step-by-step instructions, and especially when you carry out the constructions in the second part. In the words of Hartmut Endlich, “Making Platonic solids is fun and easy.”
Dr. Hartmut Endlich is a physician specializing in General Medicine and Anthroposophical Medicine, author, and speaker. As a co-founder of the Michael Healing Center in Hirschhorn and Fascia Renew, he is dedicated to a holistic approach to human health and well-being.
More Michael Heilzentrum
See also Healing Color Chambers, Goetheanum Weekly, October 19, 2023
Translation Joshua Kelberman
Footnotes
- Hartmut Endlich, Das Pentagon-Dodekaeder als strukturgebendes Maß des Menschen [The pentagonal dodecahedron as a structural measure of the human being] (Hirschhorn am Neckar, Germany: Mani Verlag, 2024).
- The Johannesbau, lit. “John Building,” named after the character of Johannes in Steiner’s Mystery Dramas, would later be transferred to Dornach and named the Goetheanum—Translator’s note.
- Cubus X is a geometric “toy” or study tool, a type of invertible cube, made from a cardboard or plastic cube articulated into 12 irregular tetrahedra connected by hinges, which then allows for a variety of spatial transformations—Tr. note.
