Let's start by drawing the described polyhedron. We are told that it has 2 hexagonal faces and 12 triangular faces.
Eachhexagon contributes six edges. Moreover, there are six edges that connect each pair of corresponding vertices of the hexagons. Furthermore, there are six edges that connect noncorresponding vertices of the hexagons.
Next, we can find the number of edges of the solid.
6+ 6+ 6+ 6= 24
Note that the solid has 2+12= 14 faces. Finally, let's recall Euler's Formula for 3-D figures.
F+V=E+2
Here, F is the number of faces, V the number of vertices, and E the number of edges of the solid. To find the number of vertices of our solid, we can substitute F= 14 and E= 24 in the above formula, and solve for V.
