Tessellating the Platonic Solids

Tessellations ◽  
2020 ◽  
pp. 341-358
Author(s):  
Robert Fathauer
Keyword(s):  
Platonic Solids

Platonic entanglement

2021 ◽  
Vol 21 (13&14) ◽  
pp. 1081-1090
Author(s):  
Jose I. Latorre ◽  
German Sierra
Keyword(s):  
Prime Number ◽  
Quantum State ◽  
Entangled States ◽  
Platonic Solid ◽  
Platonic Solids ◽  
Reed Solomon Codes ◽  
Tensor Networks

We present a construction of highly entangled states defined on the topology of a platonic solid using tensor networks based on ancillary Absolute Maximally Entangled (AME) states. We illustrate the idea using the example of a quantum state based on AME(5,2) over a dodecahedron. We analyze the entropy of such states on many different partitions, and observe that they come on integer numbers and are almost maximal. We also observe that all platonic solids accept the construction of AME states based on Reed-Solomon codes since their number of facets, vertices and edges are always a prime number plus one.

scholarly journals Study of Plasmonic Resonances on Platonic Solids

Radio Science ◽  
2017 ◽  
Vol 52 (12) ◽  
pp. 1450-1457 ◽  
Author(s):  
Dimitrios C. Tzarouchis ◽  
Pasi Ylä-Oijala ◽  
Ari Sihvola
Keyword(s):  
Platonic Solids

The Platonic Solids

2010 ◽  
pp. 141-144
Author(s):  
Nuno Crato
Keyword(s):  
Platonic Solids

The Five Platonic Solids

2021 ◽  
pp. 171-189
Author(s):  
Kristopher Tapp
Keyword(s):  
Platonic Solids

Where’s Number Four?: The Place of Structure in Plato’s Timaeus

2021 ◽  
pp. 166-180
Author(s):  
Nathan Brown
Keyword(s):  
Geometrical Structure ◽  
Platonic Solids ◽  
Platonic Theory ◽  
The Ideal

Through a detailed reading of the Timaeus, I show that the concept of structure plays an implicitly central but untheorized role in Plato’s philosophy. Plato holds apart form and matter, while theorizing the participation of particulars in universal ideas. I argue that “structure” is the concept necessary to understand the doctrine of participation, and that it mediates between the ideal and the material, the formal and the physical, in Platonic theory. This argument is developed through an engagement with the theory of the so-called Platonic solids in the Timaeus: Plato’s account of the geometrical structure of the elements. The chapter concludes by positioning this theory of structure in relation to Badiou’s “Mark and Lack” and Derrida’s Introduction to Husserl’s Origin of Geometry.

The Periodic System

2019 ◽  
Author(s):  
Eric Scerri
Keyword(s):  
Middle Ages ◽  
Point Of View ◽  
Platonic Solid ◽  
Ancient Greek ◽  
Platonic Solids ◽  
System P ◽  
Chemical Inertness ◽  
Dimensional Shape ◽  
The Many

In ancient Greek times, philosophers recognized just four elements—earth, water, air, and fire—all of which survive in the astrological classification of the 12 signs of the zodiac. At least some of these philosophers believed that these different elements consisted of microscopic components with differing shapes and that this explained the various properties of the elements. These shapes or structures were believed to be in the form of Platonic solids (figure 1.1) made up entirely of the same two-dimensional shape. The Greeks believed that earth consisted of microscopic cubic particles, which explained why it was difficult to move earth. Meanwhile, the liquidity of water was explained by an appeal to the smoother shape possessed by the icosahedron, while fire was said to be painful to the touch because it consisted of the sharp particles in the form of tetrahedra. Air was thought to consist of octahedra since that was the only remaining Platonic solid. A little later, a fifth Platonic solid, the dodecahedron, was discovered, and this led to the proposal that there might be a fifth element or “quintessence,” which also became known as ether. Although the notion that elements are made up of Platonic solids is regarded as incorrect from a modern point of view, it is the origin of the very fruitful notion that macroscopic properties of substances are governed by the structures of the microscopic components of which they are comprised. These “elements” survived well into the Middle Ages and beyond, augmented with a few others discovered by the alchemists, the precursors of modern-day chemists. One of the many goals of the alchemists seems to have been the transmutation of elements. Not surprisingly, perhaps, the particular transmutation that most enticed them was the attempt to change the base metal lead into the noble metal gold, whose unusual color, rarity, and chemical inertness have made it one of the most treasured substances since the dawn of civilization.

Interstellar Overdrive

2020 ◽  
pp. 58-66
Author(s):  
Nicholas Mee
Keyword(s):  
String Theory ◽  
Laws Of Nature ◽  
Platonic Solids ◽  
Symmetrical Shape ◽  
Regular Arrangement ◽  
Spatial Dimensions ◽  
The Universe

Kepler sought patterns and symmetry in the laws of nature. In 1611 he wrote a booklet, De Niva Sexangular (The Six-Cornered Snowflake), in which he attempted to explain the structure of familiar symmetrical objects. Almost 300 years before the existence of atoms was definitively established, he concluded that the symmetrical shape of crystals is due to the regular arrangement of the atoms of which they are formed. He also investigated the structure of geometrical objects such as the Platonic solids and the regular stellated polyhedra, known today as the Kepler–Poinsot polyhedra. Like Kepler, today’s theoretical physicists are seeking patterns and symmetries that explain the universe. According to string theorists, the universe includes six extra hidden spatial dimensions, forming a shape known as a Calabi–Yau manifold. No-one knows whether string theory will revolutionize physics like Kepler’s brilliant insights, or whether it will turn out to be a red herring.

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