Determine the vertex number of a polyhedron with six quadrancular faces

A polyhedron with six quadrilateral faces is a type of polyhedron called a **hexahedron**. Hexahedra are three-dimensional shapes with six faces. If we know that each face is a quadrilateral, it means each face is a four-sided polygon. To determine the number of vertices in a hexahedron, we'll follow these steps: 1. **Euler's Formula for Polyhedra:** Euler's formula relates the number of vertices (V), edges (E), and faces (F) of a polyhedron. It is given by: V - E + F = 2 For a hexahedron, we know F = 6, because there are six faces. We're trying to find V, so we have: V - E + 6 = 2 2. **Determine the Number of Edges:** Since each face is a quadrilateral (four-sided polygon), each face has four edges. Therefore, the total number of edges in a hexahedron is: E = 4 * 6 = 24 3. **Substitute E into Euler's Formula:** Plugging in E = 24, we have: V - 24 + 6 = 2 4. **Solve for V:** Rearrange the equation to isolate V: V - 18 = 2 V = 20 So, a hexahedron (polyhedron with six quadrilateral faces) has 20 vertices.