SOLUTION: A decagonal trapezohedron has 20 faces, each of which is a kite. How many vertices are there on a decagonal trapezohedron?

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Question 1180622: A decagonal trapezohedron has 20 faces, each of
which is a kite. How many vertices are there on a
decagonal trapezohedron?
Found 3 solutions by MathLover1, ikleyn, greenestamps:
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!

Set of trapezohedra faces kites, edges , and vertices
if a decagonal trapezohedron has faces, then

then the number of vertices is

there are vertices on a decagonal trapezohedron

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.

        On a decagonal trapezohedron, see this link

https://en.wikipedia.org/wiki/Decagonal_trapezohedron

                    and also

https://en.wikipedia.org/wiki/Trapezohedron

Find there a picture (a Figure) and all associated information.

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

One tutor apparently quoted a reference to show the answer; another pointed you to a reference where you can find the answer.

An alternative to that approach is to do some math and get some practice in problem-solving skills.

The figure has 20 faces, each of which is a kite. The 20 kites together have a total of 20*4=80 edges. An edge of the solid is where the edges of two faces meet. The number of edges is therefore 80/2=40.

Then use Euler's formula to determine the number of vertices:

E = V+F-2
40 = V+20-2
V = 22

ANSWER: this solid has 22 vertices.