A solid has 10 faces: 4 triangles;1 Square; 4 hexagons; and 1 octagon, how many vertices does the solid have?
it is 19 or 20 choose wisely
the anwser is 19
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To calculate the number of vertices of a solid, we need to determine how many corners or meeting points exist.
In this case, we have 4 triangles. Each triangle has 3 vertices, so the triangles contribute 4 x 3 = 12 vertices.
We also have 1 square with 4 vertices.
Next, we have 4 hexagons. Each hexagon has 6 vertices, so the hexagons contribute 4 x 6 = 24 vertices.
Finally, we have 1 octagon with 8 vertices.
To find the total number of vertices, we add up the contributions from each shape:
12 (from the triangles) + 4 (from the square) + 24 (from the hexagons) + 8 (from the octagon) = 48 vertices.
Therefore, the solid has 48 vertices in total.
Euler showed that F+V-E=2, so now we know that
E-V = 10
Since each edge belongs to two polygons, there are (4*3+1*4+4*6+1*8)/2 = 24 edges
So, there are 14 vertices
seems reasonable, since all vertices belong to 3 or mlore polygons