Verify Euler's relation for each of the following:
A. A cube
B. A tetrahedron
C. A triangular prism
D. A square pyramid
A.
According to Euler’s Formula
F + V –E = 2
Where F denotes the number of face
V denotes the number of vertices
E denotes the number of edges.
Shape | Faces | Vertices | Edges | F + V – E |
Cube | 6 | 8 | 12 | 2 |
B.
According to Euler’s Formula
F + V –E = 2
Where F denotes the number of face
V denotes the number of vertices
E denotes the number of edges.
Shape | Faces | Vertices | Edges | F + V – E |
Tetrahedron | 4 | 4 | 8 | 2 |
C.
According to Euler’s Formula
F + V –E = 2
Where F denotes the number of face
V denotes the number of vertices
E denotes the number of edges.
Shape | Faces | Vertices | Edges | F + V – E |
Triangular Prism | 5 | 6 | 9 | 2 |
D.
According to Euler’s Formula
F + V –E = 2
Where F denotes the number of face
V denotes the number of vertices
E denotes the number of edges.
Shape | Faces | Vertices | Edges | F + V – E |
Square Pyramid | 5 | 5 | 8 | 2 |