How many vertices does a nonahedron have?

Answer 1

A nonahedron is a nine-faced polyhedron, also known as an enneahedron. The number of vertices in a nonahedron can be calculated using Euler's formula, which states that for any polyhedron, the number of vertices (V), edges (E), and faces (F) are related by the equation V - E + F = 2. A nonahedron has 9 faces, so substituting F = 9 into the formula gives V - E + 9 = 2. Since the nonahedron has 9 faces and each face is a polygon with 3 sides, the total number of edges is 9 * 3 / 2 = 13. Therefore, the number of vertices in a nonahedron can be calculated as V - 13 + 9 = 2, which simplifies to V = 6.

Answer 2

There are 2606 distinct convex nonahedrons with varying numbers of vertices, such as Johnson solid #14 (a triangular prism sandwiched between two pyramids) which has 8, and the heptagonal prism with 14. Concave solids could have even more!