CK-12 Geometry-Concepts

11.1. Polyhedrons http://www.ck12.org

Example C

In a six-faced polyhedron, there are 10 edges. How many vertices does the polyhedron have?

Solve forVin Euler’s Theorem.

F+V=E+ 2

6 +V= 10 + 2

V= 6 There are 6 vertices.

Watch this video for help with the Examples above.

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/52631

CK-12 Foundation: Chapter11PolyhedronsB

Vocabulary

Apolyhedronis a 3-dimensional figure that is formed by polygons that enclose a region in space. Each polygon in a
polyhedron is aface.The line segment where two faces intersect is anedge.The point of intersection of two edges
is avertex.Aregular polyhedronis a polyhedron where all the faces are congruent regular polygons.

Guided Practice

1. In a six-faced polyhedron, there are 10 edges. How many vertices does the polyhedron have?


2. Markus counts the edges, faces, and vertices of a polyhedron. He comes up with 10 vertices, 5 faces, and 12
   edges. Did he make a mistake?


3. Is this a polyhedron? Explain.

Answers:

1. Solve forVin Euler’s Theorem.

F+V=E+ 2

6 +V= 10 + 2

V= 6