What is this website all about? It is pointing to a science of the future. A science that studies the objective structure of a manifested form and explores the form’s basic intention. This site provides only one example of how this can come about. Frank is an artist, sculptor and geometrician who lives in San Francisco. He has taught art for more than thirty years in high schools and colleges. Since encountering the work of Rudolf Steiner, Frank has been exploring the relation between form and spirit. This has led him to take up research concerning the number seven, and in 2000 he discovered a new geometric form never seen before. Putting this form through the alchemical transformative process of Earth, Water, Air, and Fire, many previously unknown geometric structures have emerged. Also this geometric form demonstrates a remarkable correlation to the form and functioning of the human heart. On the basis of experimentation with various related geometric forms and the movement of water in a vortex, Frank is uncovering indications concerning the relationship between etheric formative forces and the geometry, structure, and physiology of the human heart. Thus the form is called the Chestahedron, both after its discoverer and because the form relates to the geometry of the heart, which sits in the chest.

For the last several years he has been teaching sacred geometry at the Waldorf teacher training program in San Francisco. He has been presenting his research at international conferences and Waldorf schools in the United States and Europe.

Why was the Chestahedron not found before? People have been working with Platonic solids for thousands of years, including such great figures as Pythagoras, Plato, Kepler, Da Vinci, and many others. As in the past and up to this day, all studies of transforming Platonic solids have been based upon pressure/contraction. This approach utilizes truncations, which refers to cutting off or pushing existing corners flat in order to change a form. Frank’s approach to studying Platonic solids was not transforming them externally by contraction but internally by expansion. Platonic forms were never solid to Frank, but open and hollow. Placing a small Tetrahedron inside a larger Tetrahedron, twice its size, and moving the smaller form produces the Chestahedron, something of which the world has never seen before in the long history of form studies. Surprisingly, the Chestahedron can show an internal transformation moving in two opposite directions at the same time. These motions, when related to physiology, provide a picture of how the human heart is formed out of two opposite moving vortexes: the blood. Thus, there is a design concept behind the geometry connected with the human heart. The heart is working not simply through the utilization of pressure (pumping) but by suction (breaking) arising when two vortexes entwine together from opposite directions. As amazing as the above findings are, it does not explain how the Chestahedron was originally discovered. All the five Platonic forms have an even number of faces, but the Chestahedron has an odd number of faces with equal surface areas, making it difficult to discover even with today’s technology. That is why a heptahedron with equal surface areas like the Chestahedron was not discovered before. Frank used a mathematical approach first but couldn’t make it work — the form eluded him. He encountered an obstacle with odd numbers, which mathematics in the past could not overcome. To solve this problem Frank used his background as an artist and developed an artistic procedure specifically designed for new form research. His background as a trained and working artist has allowed him to develop flexibility in thinking, intuition and creativity. Moving from objective, mathematical approaches to artistic approaches and back engendered a creative tension that kept the research from becoming either too constricted or too loose. The result was that Frank was able not only to discover the Chestahedron and myriad related forms, but has been able to slowly uncover their significance, bringing to the world an extension and furtherance of principles of sacred geometry and the mysterious relationship between form and spirit.

Seth Miller

M.A. Consciousness Studies, Ph.D.c. Transformative Studies

Frank’s work helps crack open new avenues of thinking, new ways of understanding our world, and provides insights that help us better understand ourselves. What he is doing, in a nutshell, is exploring the relationship between geometric form and the dynamic principles that underlie the operations of natural and physiological processes, specifically those related to the human being. He did not set out with this goal in mind, but rather followed the trail of a simple question concerning the possibility of a seven-sided geometric form with faces of equal surface area. As a sculptor, Frank didn’t just think about this idea, he made it – “it” in this case being a new geometric form that had never before been discovered. The significance of this is not just that such a form exists, but that the form has meaningful relationships to other phenomenon which are unveiled through a particular way of engaging with the research process itself. In other words, the significance of Frank’s achievements lie equally in the realm of the process by which his discoveries were made as in the discoveries themselves. Frank’s work is moldbreaking in a very important way, and this is in terms of the process by which he does his work. The standard methods by which science builds upon itself have some significant blind spots and assumptions that have historically limited its potential (and created some nasty problems along the way, even while helping elsewhere). Most significantly, the methodologies used are generally designed to eliminate what is innately human from the research process, in an attempt to ‘control’ the situation so that results fit within the assumptions of the experimental design. This style of research provides a certain kind of answer: answers which are geared towards application through reductionistic analysis and control of component parts.

Such approaches, and the answers they provide, are proving to be less and less able to provide fruitful metaphors for a sustainable future. Frank’s work exemplifies an approach that helps bridge this entrenched gap, bringing forth a soulfully engaged style of research that weaves between art and science, allowing the strengths of each to fructify the weaknesses of the other. The result is an integrated style of research that can comfortably deal with both the ‘outer’ and the ‘inner’, without over-privileging one or disparaging the other. In addition to this, his work is moldbreaking in that it constitutes a modern extension of the tradition of sacred geometry, providing a number of well-grounded insights that testify to the integration between humans and the laws of the cosmos.


This website has benefited from the time, skills, and support of many individuals. Thanks to them it has been possible to present Frank’s work to a wider audience, with the hope that his efforts will inspire others.  |  Jim Willetts  |  Kaye Williams  |  Dottie Zold  |  Raphael Medical Foundation  |  ADCO Outdoor Advertising

pmdworks | Seth Miller, Spirit Alchemy Design  |  Stefan Klocek

Jim Heath  |  Dana Rossini Rogers

Windy Allen  |  Tomas Howell, Slate Mountain Studio  |  John Swain

Steven Mathias