Answer:
(a) No
(b) No
(c) No
Step-by-step explanation:
Given
See attachment
Required
Select Yes or No for each
To do this, we make use of Euler's formula
[tex]F + V - E = 2[/tex]
Where
[tex]F \to Faces; V \to Vertices; E \to Edges[/tex]
[tex](a):\ Faces = 8; Vertices = 12; Edges = 6[/tex]
Using: [tex]F + V - E = 2[/tex]
[tex]8 + 12 - 6 = 2[/tex]
[tex]14 = 2[/tex]
The above equality is false. Hence, (a) does not exist
[tex](b):\ Faces = 6; Vertices = 6; Edges = 4[/tex]
Using: [tex]F + V - E = 2[/tex]
[tex]6 + 6 - 4 = 2[/tex]
[tex]8 = 2[/tex]
The above equality is false. Hence, (b) does not exist
[tex](c):\ Faces = 20; Vertices = 30; Edges = 12[/tex]
Using: [tex]F + V - E = 2[/tex]
[tex]20 + 30 - 12 = 2[/tex]
[tex]38 = 2[/tex]
The above equality is false. Hence, (c) does not exist
