For each of the 5 regular polyhedra, recall that one can inscribe a polyhedron inside as follows. For each of the faces of the original polyhedron, create a vertex at the center of that face (i.e. the point which is equidistant from all the vertices of that face). Now connect two vertices if their corresponding faces have a boundary line in common. This way we created the vertices and faces of our new polyhedron. Fact. This new polyhedron is again a regular polyhedron. (Feel free to try and figure out why.) Problem 2. Given three points in the plane, we can construct two half-lines as in the picture below, creating an angle 0. Construct, with ruler and compass, a line that cuts the angle in half. Describe your construction and explain why it divides 0 into two equal angles.
For each of the 5 regular polyhedra, recall that one can inscribe a polyhedron inside as follows. For each of the faces of the original polyhedron, create a vertex at the center of that face (i.e. the point which is equidistant from all the vertices of that face). Now connect two vertices if their corresponding faces have a boundary line in common. This way we created the vertices and faces of our new polyhedron. Fact. This new polyhedron is again a regular polyhedron. (Feel free to try and figure out why.) Problem 2. Given three points in the plane, we can construct two half-lines as in the picture below, creating an angle 0. Construct, with ruler and compass, a line that cuts the angle in half. Describe your construction and explain why it divides 0 into two equal angles.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:For each of the 5 regular polyhedra, recall that one can inscribe a polyhedron inside as follows. For each
of the faces of the original polyhedron, create a vertex at the center of that face (i.e. the point which is
equidistant from all the vertices of that face). Now connect two vertices if their corresponding faces have
a boundary line in common. This way we created the vertices and faces of our new polyhedron.
Fact. This new polyhedron is again a regular polyhedron. (Feel free to try and figure out why.)
Problem 2. Given three points in the plane, we can construct two half-lines as in the picture below,
creating an angle 0. Construct, with ruler and compass, a line that cuts the angle in half. Describe your
construction and explain why it divides 0 into two equal angles.
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