# Platonic Solids

What happens when space crystallises and points begin to arrange themselves into a sphere Why were primordial sages fascinated with five simple forms How does the threedimensional jigsaw fit together Why is this truly universal science An understanding of the Platonic Solids, and their close cousins, the Archimedean Solids has long been required of students seeking entry into ancient wizdom schools. This book, illustrated by the author, is a beautiful introduction to threedimensional mathemagical space.- written and illustrated by Daud Sutton platonic Archimedean Solids First published in a less excell
- In The Name of God, The Compassionate, The Merciful. This book is dedicated to Professor Keith Critc
- 1 IntroductIon Imagine a sphere. It is Unitys perfect symbol. Each point on its surface is identic
- 3 2 Imagine you are on a desert island there are sticks, stones and sheets of bark. If you start e
- 5 4 The tetrahedron is composed of four equilateral triangles, with three meeting at every vertex.
- 7 6 the octahedron 8 faces 12 edges 6 vertices The octahedron is made of eight equilateral triangl
- 9 8 The icosahedron is composed of twenty equilateral triangles, five to a vertex. It has fifteen 2
- 11 10 the cube 6 faces 12 edges 8 vertices The cube has octahedral symmetry below. Plato assigned
- 13 12 the dodecahedron 12 faces 30 edges 20 vertices The beautiful dodecahedron has twelve regular
- 15 14 a Short Proof are there really only five A regular polygon has equal sides and angles. A regu
- 16 17 all thIngS In PaIrS platonic solids two by two What happens if we join the facecentres of the
- 19 18 around the globe in elegant ways Platos cosmology constructs the Elemental Solids from two typ
- 21 20 round and round lesser circles Any navigator will tell you that the shortest distance between
- 23 22 the golden ratIo and some intriguing juxtapositions Dividing a line so that the shorter sectio
- 25 24 Polyhedra wIthIn Polyhedra and so proceed ad infinitum The Platonic Solids fit together in rem
- 27 26 comPound Polyhedra a stretch of the imagination The interrelationships on the previous page ge
- 29 28 the KePler Polyhedra the stellated great stellated dodecahedron The sides of some polygons ca
- 31 30 the PoInSot Polyhedra the great dodecahedron great icosahedron Louis Poinsot 17771859 investi
- 33 32 the archImedean SolIdS thirteen semiregular polyhedra The thirteen Archimedean Solids opposite
- 35 34 fIve truncatIonS off with their corners Truncate the Platonic Solids to produce the five equal
- 37 36 the cuboctahedron 14 faces 24 edges 12 vertices The cuboctahedron combines the six square fa
- 39 38 a cunnIng twISt and a structural wonder Picture a cuboctahedron made of rigid struts joined at
- 41 40 the IcoSIdodecahedron 32 faces 60 edges 30 vertices The icosidodecahedron combines the twelv
- 43 42 four exPloSIonS expanding from the centre Exploding the faces of the cube or the octahedron ou
- 45 44 turnIng the snub cube snub dodecahedron The name snub cube is a loose translation of Keplers
- 47 46 the archImedean dualS everything has its opposite The duals of the Archimedean Solids were fir
- more exPloSIonS and unseen dimensions 49 48 Exploding the rhombic dodecahedron, or its dual the cubo
- 51 50 flatPacKed Polyhedra If a polyhedron is undone along some of its edges and folded flat, the re
- 53 52 archImedean SymmetrIeS The diagrams below show the rotation symmetries of the Archimedean Soli
- Volume r 3 s 3 s 3 s 3 2 s 3 4 s 3 A recurring theme in the metric properties of
- Tetrahedron Cube Octahedron Dodecahedron Icosahedron Stellated Dodecahedron Great Dodecahedron Grea
- If you have enjoyed this Wooden Book others in the series which may be of interest include Sacred Ge