document.write( "Question 142837This question is from textbook geometry
\n" ); document.write( ": determine the number of face vertices and edges of the solids \n" ); document.write( "

Algebra.Com's Answer #103928 by MathLover1(20850) $\"\"$ $\"About$

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notice that:
\n" ); document.write( "Each solid has flat sides called $\"faces\"$ .
\n" ); document.write( "Each solid has $\"edges\"$ to connect the faces.
\n" ); document.write( "Each solid has $\"vertices+\"$ that connect the edges. \r
\n" ); document.write( "\n" ); document.write( "There are $\"many\"$ different $\"solid\"$ $\"+shapes\"$ that are $\"polyhedra\"$ . You can examine the shapes and count the number of faces, edges, and vertices for each. \r
\n" ); document.write( "\n" ); document.write( "There are $\"only\"$ $\"+five\"$ regular polyhedra. This means that there are only five solids in which
\n" ); document.write( "all of the faces are congruent regular polygons. \r
\n" ); document.write( "\n" ); document.write( "These five regular polyhedra are called the $\"Platonic\"$ $\"+Solids\"$ . The Platonic Solids are:
\n" ); document.write( "the $\"tetrahedron\"$ which has 4 equilateral triangles as faces;
\n" ); document.write( "the $\"hexahedron\"$ which has 6 squares as faces;
\n" ); document.write( "the $\"octahedron\"$ which has 8 equilateral triangles as faces;
\n" ); document.write( "the $\"dodecahedron\"$ which has 12 equilateral pentagons as faces;
\n" ); document.write( "and the $\"icosahedron\"$ which has 20 triangles as faces.\r
\n" ); document.write( "\n" ); document.write( "Euler characteristic: there is a relation among the number of edges $\"E\"$ , vertices $\"V\"$ , faces $\"F\"$
\n" ); document.write( " $\"x=V+-+E+%2B+F=2+\"$ This result is known as $\"Euler%27s\"$ $\"+formula\"$ , and can be applied not only to polyhedra but also to embedded planar graphs.
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