a regular octahedron is a polyhedron with 9 faces true or false
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.
FALSE
False.
A regular octahedron is a polyhedron, but it has 8 faces, not 9.
To verify this, you can use the formula for the number of faces in a polyhedron, which is given as Euler's formula: F + V = E + 2. In this formula, F represents the number of faces, V represents the number of vertices, and E represents the number of edges.
For a regular octahedron, which has 6 vertices and 12 edges, we can substitute these values into the formula: F + 6 = 12 + 2. Simplifying this equation, we get F + 6 = 14, and by subtracting 6 from both sides, we find that F = 8.
Therefore, a regular octahedron has 8 faces, not 9.