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Vesna [10]
2 years ago
9

Could a polyhedron exist with the given number of faces, vertices, and edges? Drag yes or no to each combination

Mathematics
2 answers:
Bogdan [553]2 years ago
7 0

Answer:

no

NO

NO

Step-by-step explanation:

good luck have a nice day

DanielleElmas [232]2 years ago
5 0

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

F + V - E = 2

Where

F \to Faces; V \to Vertices; E \to Edges

(a):\ Faces = 8; Vertices = 12; Edges = 6

Using: F + V - E = 2

8 + 12 - 6 = 2

14 = 2

<em>The above equality is false. Hence, (a) does not exist</em>

(b):\ Faces = 6; Vertices = 6; Edges = 4

Using: F + V - E = 2

6 + 6 - 4 = 2

8 = 2

<em>The above equality is false. Hence, (b) does not exist</em>

<em />

<em />(c):\ Faces = 20; Vertices = 30; Edges = 12<em />

Using: F + V - E = 2

20 + 30 - 12 = 2

38 = 2

<em>The above equality is false. Hence, (c) does not exist</em>

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