Page 72 - NUMINO Challenge_D1
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Basic Concepts Regular Polyhedron
A regular polyhedron is a solid figure that has congruent polygon faces. In
a regular polyhedron, the same number of faces meet at each vertex.
There are five regular polyhedrons.
Tetrahedron Cube Octahedron Dodecahedron Icosahedron
Example Explain why there is no regular polyhedron that has hexagons as
side faces.
Class Notes
If 2 regular polygons are connected at one vertex and folded in the
direction of the arrow, the figure that is formed (will / will not) be a
regular polyhedron because they will completely overlap.
Therefore, at least faces must meet at one vertex to make a soild figure.
If 3 equilateral triangles are connected at one vertex, as shown below, the measure of
the angle of the vertex is 180 . If 3 squares are connected, the measure of the angle is
. If 3 regular pentagons are connected, the measure of the angle is .
If the figures are folded in the direction of the arrows, the figures that are formed
(will / will not) be regular polyhedrons.
180
If 4 equilateral triangles are connected at one vertex, the measure of the angle of the
vertex is . If 5 equilateral triangles are connected, the measure of the angle is
. If the figures are folded in the direction of the arrows, the figures that are
formed (will / will not) be regular polyhedrons.
If 3 regular hexagons are connected at one vertex, the measure of
the angle of the vertex is . The figure connected to the vertex
is completely flat, so it (can / cannot) be made into a polyhedron.
69Geometry
A regular polyhedron is a solid figure that has congruent polygon faces. In
a regular polyhedron, the same number of faces meet at each vertex.
There are five regular polyhedrons.
Tetrahedron Cube Octahedron Dodecahedron Icosahedron
Example Explain why there is no regular polyhedron that has hexagons as
side faces.
Class Notes
If 2 regular polygons are connected at one vertex and folded in the
direction of the arrow, the figure that is formed (will / will not) be a
regular polyhedron because they will completely overlap.
Therefore, at least faces must meet at one vertex to make a soild figure.
If 3 equilateral triangles are connected at one vertex, as shown below, the measure of
the angle of the vertex is 180 . If 3 squares are connected, the measure of the angle is
. If 3 regular pentagons are connected, the measure of the angle is .
If the figures are folded in the direction of the arrows, the figures that are formed
(will / will not) be regular polyhedrons.
180
If 4 equilateral triangles are connected at one vertex, the measure of the angle of the
vertex is . If 5 equilateral triangles are connected, the measure of the angle is
. If the figures are folded in the direction of the arrows, the figures that are
formed (will / will not) be regular polyhedrons.
If 3 regular hexagons are connected at one vertex, the measure of
the angle of the vertex is . The figure connected to the vertex
is completely flat, so it (can / cannot) be made into a polyhedron.
69Geometry
