The 3-Dimensional Icosahedron Periodic Table
By Dr. Chong Soo Han, Department of
and Dr. Sunah Kim Han, Department of Mathematics,
Editor’s Note: Offering a quite interesting mix of science and philosophy, the authors of this paper present a new way of perceiving the Chemical Periodic Table. Whether we hail from the hard sciences, the arts and letters, the humanities or other fields, we have all, at one time or another, encountered the Periodic Table. Presented here is a paper edited for the layperson, giving a new visual twist to what, prior to now, had always been illustrated in 2-dimension.
Since ancient times humans have wanted to transform materials, thus the early refinement of iron, the creation of brass, and so on. In their quest to transform known materials of their era, the ancients conceived the idea of elemental materials, from which a compound material was created. Thus, it was correctly thought, that if such a compound could be physically or chemically divided into its elemental units that the material could be reconstructed into a different compound. The ancients thus strove to identify the elements, and settled on the four elements of soil, water and air and fire.
About 350 BC, the Greek philosopher and mathematician, Plato, believed that the universe could be explained from the viewpoint of mathematics and he proposed five elements corresponding to five perfect solids. The perfect solids are the tetrahedron (consisting of four sides, each an equilateral triangle), the cube (six sides, each a perfect square), the octahedron (eight sides, each an equilateral triangle), the dodecahedron (12 sides, each an equilateral pentagon) and the icosahedron (20 sides, each an equilateral triangle).
The five perfect solids
In the modern era the theoretical ‘fifth element’ is no longer a topic of consideration. However, we know that in previous centuries and previous millennia scientists in both the Eastern and Western cultures believed that five elements explained the universe. As to why this belief in the existence of five elements was predominant -- regardless of place or culture -- in the ancient and pre-Einsteinian eras, it is interesting and perhaps pertinent to note that we also have five fingers, thus perhaps leading to a sort of intuitive belief in the five-element concept. If we consider that perhaps Plato had a transcendental cognition of the elements of the universe, this could be the basis for his theory of the ‘magic’ element Aether, which he believed was dodecahedron-shaped or possibly another perfect solid of a shape which can be placed inside a dodecahedron. Although Plato believed that Aether has characteristics similar to other perfect solids, he had difficulty in describing Aether in relation to the other perfect solids, because at that time the Greeks believed that the water element was sphere-shaped. Thus the icosahedron -- as the solid with a shape most similar to the sphere – was related to water, while fire was related to the edged tetrahedron, soil to the stable cube and air to the unstable octahedron. Plato may have had only a transcendent cognition that Aether might relate to a perfect solid, but without visualized evidence he could not relate it to the solid in opposition to the common belief of the era.
Following this line of thought -- and taking note of the fact that the dodecahedron has the same symmetry as the icosahedron -- the authors of this paper conceived that, as a mathematician, Plato conceptualized the inside of the dodecahedron mathematically. An icosahedron can be generated from the lines which form the centers of the faces of the dodecahedron (see illustrations, right). A mathematician would say that the dodecahedron and the icosahedron are ‘duals’, as are the octahedron and the cube. Inversely, a dodecahedron can be formed inside an icosahedron with the same method. Similarly, a tetrahedron can be formed inside a larger tetrahedron; this arrangement is referred to as a ‘self dual’. This means there is a possibility that, after recognizing that the supposed ‘fifth element’ corresponded to a solid consisting of 20 faces, Plato conceptualized an icosahedron inside a dodecahedron.
In 1871, the Russian chemist Mendeleyev organized the chemical elements known at time into eight families on the periodic table.
Mendeleyev's periodic table (1871)
At present, we know that there are 18 families and two f-block families; correspondingly, we know that the chemical elements can be classified into 20 families, thus relating to the 20-sided icosahedron.
IUPAC periodic table of chemical elements (2007)
If we contemplate two facts, one can find a similarity between the fifth element relating to the 20 faces of the icosahedron and the 20 families of the modern periodic table. In the other words, there is a possibility that, from his transcendental meditation about Aether, Plato may have intuitively known the element has 20 faces. Subsequently, modern chemists found 20 families in the elements from the viewpoint of chemical properties.
Considering the above, we know of the 20 faces
in the icosahedron for Aether from the transcendental meditation of Plato, and modern
science divides the currently-known elements into 20 families. Conceptualizing what follows requires a jump in one’s thinking.
We are parts of the universe and our nature is the same to that of the
universe. This means that if one opens one’s mind philosophically, departing
from the viewpoints of traditional education and preconceived ideas, one can
see the nature of universe. This is the basis of meditation in Buddhism. In the
authors’ knowledge, Kant thought about this matter and he mentioned ‘the
transcendental knowledge’. Many inspirations of great scientific discovery are
achieved in this manner; in fact, Albert Einstein once said that he developed
his Theory of Relativity by visualizing himself sitting on a photon as it
dashed through space. The authors of this paper posit that Plato (and along
with him, Mendeleyev) also had a brilliant clarity of mind, enabling him to
visualize the structure of chemical elements. This brings us to a fundamental
philosophical question: “Can one find a thing which does not exist in the
The features of the icosahedron 3-D periodic table are as follows:
1. We can touch it. This stimulates one’s interest in the elements, relating to chemistry as well as to science in general, from young children taking their first look at chemistry to professional scientists teaching the subject.
2. In the basic model, the f-block elements are located in their correct position1.
There are many symmetry operations2 in the icosahedron. When one is playing with the 3D periodic table, one’s spatial perception is greatly enhanced.
3. One can handily rearrange the periodic table depending upon one’s particular interest or experimentation. This is the authors’ proposal for the next generation of chemists, teachers and students. The authors posit that future generations will be able to change the chemical properties of the elements and, correspondingly, they will change the location of the families on the faces of icosahedron. This change, however, does not mean they will be able to change the elements themselves as the Alchemists attempted.
In conclusion, the authors of this paper believe that if there are other intellectual living things in the universe, they too will begin their journey of scientific discovery with the recognition of five perfect solids3 and the periodicity of chemical properties4 of the elements. We believe they will group the elements into a periodic table as Mendeleyev did. And finally they will make 3-D icosahedron periodic tables to teach science to their children.
This figure below serves as a visual summary of the paper:
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