convex polyhedron is made out of equilateral triangles and regular pentagons_ Five faces meet at each vertex; including at least one triangle and at least one pentagon. Determine the number of vertices, faces; and edges in the polyhedron_
Added by Jose Ramon B.
Close
Step 1
Since five faces meet at each vertex, and each face is either a triangle or a pentagon, we can say that at each vertex there is at least one triangle and one pentagon. This means that each vertex is shared by 3 triangles and 2 pentagons, or 2 triangles and 3 Show more…
Show all steps
Your feedback will help us improve your experience
Dayna Kitsuwa and 85 other Geometry educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Geometry In the regular polyhedron described below, all faces are congruent polygons. Use a system of three linear equations to find the numbers of vertices, edges, and faces. Every face has five edges and every edge is shared by two faces. Every face has five vertices and every vertex is shared by three faces. The sum of the number of vertices and faces is two more than the number of edges.
Linear Systems
Systems with Three Variables
For a regular tetrahedron, find the number of faces, vertices, and edges in the polyhedron. Then verify Euler's equation for that polyhedron.
Surfaces and Solids
Polyhedrons and Spheres
The polyhedron below is formed by taking a square prism and placing a square pyramid on top of it. The triangles that form the pyramid on top of the prism are all equilateral triangles. Draw the net for the polyhedron in the diagram.
Kari H.
Recommended Textbooks
Geometry A Common Core Curriculum
Geometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD