The Platonic Solids

Discovery 1: How many Platonic Solids exist in this world?
Materials:[br]Regular geometric tiles (i.e., equilateral triangles, squares, pentagons, and hexagons)[br][br]The Challenge: Construct a 3D corner (vertex) using only one type of regular polygon. How many can you find?[br][br][br][br]Concept focus:[br]A Platonic Solid is a 3D shape where[br][list][*]each face is the same regular polygon[/*][*]the same number of polygons meet at each vertex (corner)[/*][*]The total angle at each vertex must be less than 360°[/*][/list]
Discovery 2: Pattern Recognition
Group Activity:[br][list=1][*]Each group builds a Platonic solid using recycled materials (i.e., straw for edges, cardboard for faces)[/*][*]Create a table of values that show the number of vertices, edges, and faces for each solid.[/*][/list][br]Analysis:[br]Look at the numbers for each solid. Test the Euler's Formula for each solid, [b]V - E + F = 2[/b].[br]Does the values for each solid satisfy the equation?[br][br]Alternatively, you may explore the digital solids below.
Tetrahedron
Hexahedron / Cube
Octahedron
Dodecahedron
Icosahedron
Properties & Conditions for Building Platonic Solids
[b]Polyhedron Criteria:[br][/b][list][*][b]Euler’s Characteristic [/b]- The solid must satisfy the formula V - E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces.[/*][/list][br][b]Regular Polyhedron Criteria:[br][/b][list][*][b]Face regularity [/b]- All faces must be congruent regular polygons.[/*][*][b]Vertex regularity [/b]- The same number of faces must meet at every vertex in exactly the same arrangement[b][br]Convexity [/b]- The solid must be convex (line segment test); If you pick any two points inside the shape, the line connecting them stay entirely inside the shape[/*][/list][b]Platonic Solid Criteria:[/b][br][list][*][b]The 360[sup]o[/sup] Limit[/b] - If you sum the interior angles of the polygons meeting at a vertex, the total must be less than 360[sup]o[/sup] .[/*][/list]
[i][size=85][b]Solution[/b][br]Discovery 1: Only 3, 4, or 5 triangles, 3 squares and 3 pentagons work. If you join 6 triangles or 3 hexagons, it creates a flat 360[sup]o[/sup] surface, so they cannot fold into a solid. Which lead to a conclusion why only five exist.[br][br]Discovery 2: It is impossible to have more than 5 platonic solids, because any other possibility violates or does not satisfy the number of edges, corners and faces according to Euler's Formula.[/size][/i]
1. Verify if the following solid is a Platonic solid.[br][img]data:image/png;base64,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[/img]
1. Verify if the following solid is a Platonic solid.[br][img]data:image/png;base64,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[/img]
3. Verify if the following solid is a Platonic solid.[br][img]data:image/png;base64,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[/img]
4. Verify if the following solid is a Platonic solid.[br][img]data:image/png;base64,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[/img]
Duality in Platonic Solids
Materials: 3D models / Diagrams of the 5 Platonic Solids[br]Perform the following steps for each solid:[br][list=1][*]Mark the center point of every face.[/*][*]Imagine or physically connect using string/wire/ drawing these center points to form a new internal solid.[/*][*]Compare the new solid formed inside the initial solid.[/*][/list][br]Focus:[br]Each platonic solid has a pair that fits within each other in geometric harmony.[br]There is a relationship between the duality of each solid (the initial & the new solid formed inside the initial solid):[br][list][*]vertices & faces: the number of faces of the initial solid equals the number of vertices of the new, and vice-versa (i.e., a Cube with 6 faces & 8 vertices creates an Octahedron with 8 faces & 6 vertices inside it).[/*][*]edges: dual pairs have the same number of edges.[/*][*]a solid can be perfectly inscribed inside its dual partner, where the vertices touch the centers of the faces of the outer solid.[/*][/list]Tetrahedron is self-dual; Cube & Octahedron are dual pairs; Dodecahedron & Icosahedron are dual pairs[i][br][img]https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPOuc01eV2lep7BZQ_njK2K0FR8-nyOH6Z9eirpY8EoEf9VfWlPdcrmcRrihYLemVlfaICtac2Jmaf0Kay_tZYcYDmRGRUmnaC-pThZe9CPwWk-CqQufIUjMcq0LKK-5VAZvgWz6f-YpL6/s400/PLATONIC+SOLIDS-2.jpg[/img][/i]
Surface Area
Use the fundamental geometry of a regular [i][math]n[/math][/i]-gon and build the formula.[br][br]For any regular polygon with [i][math]n[/math][/i] sides of length [i][math]a[/math][/i], the area of the polygon is given by[br]Area of polygon [math]=\frac{1}{2}\times Perimeter\times apothem[/math][br]For a triangle ([math]n=3[/math]), this simplifies to area = [math]\frac{\sqrt{3}}{4}a^2[/math].[br]Find the surface area for a tetrahedron, cube, octahedron, dodecahedron, and icosahedron with length [math]a[/math].
Volume
The volume formula is derived from the idea that any Platonic solid can be divided equally into [math]n[/math] equal pyramids.[br][br]Each pyramid has[br][list][*]base = 1 face of the solid[/*][*]apex = center of the solid[/*][*]height = distance from the center of the solid to the center of the face[/*][/list]Therefore, the volume for any Platonic solid is[br][math]V_{pyramid}=\frac{1}{3}\times BaseArea\times height[/math]
Fermer

Information: The Platonic Solids