Question

Mario’s company makes unusually shaped imitation gemstones. One gemstone has 12 faces and 11 vertices. How many edges does the gemstone have?

Answer 1

using Polyhedral formula (v;vertices, e;edges, f;faces) v + f - 2 = e

v=11 f=12
11+12-2=21

21 edges

Answer 2

21 edges does the gemstone have

Explanation:

By Leonard Euler's Polyhedral Formula:

`v+f-2 = e` .....[1]

where,

v is the vertices

f is the faces

e is the edges.

As per the statement:

Mario’s company makes unusually shaped imitation gemstones.

One gemstone has 12 faces and 11 vertices.

⇒f = 12 and v = 11

Substitute these in [1] we have;

`11+12-2 = e`

⇒
`23-2 = e`

Simplify:

⇒
`21= e`

Therefore, 21 edges does the gemstone have