How man vertices on a octangualar pyramid?

Answer 1

Answer 3

Of course it depends on the shape. And the question is about one particular shape: an octangular (let's not quibble over the spelling) pyramid. This is by definition a shape having an octagon as its base and one apex. The base has 8 vertices and the apex is the 9th.

Answer 2

It depends on the shape.

Octangular implies 8 vertices. These can be in the form of a cuboid, a heptagonal pyramid, a hexagonal di-pyramid, or at least two other shapes.

A cuboid has 16 diagonals;

A heptagonal pyramid has 14 (all in the heptagon);

A hexagonal dipyramid had 10 (9 in the hexagon and one joining the two apex).

The "other shapes".

Think of a triangular prisms lying on a rectangular face. Consider both the top vertices being pushed towards each other. Now attach this to a mirror image underneath it. This shape will have 14 diagonals. (If the vertices are not pushed in, the result will be a kind of cuboid).

Finally, there as a pentagon with one apex below it and two apex above. There are 5 diagonals in the pentagon, 5 from the pentagon to an apex above, two between the top apex and bottom and none between the pentagon and the apex below. A total of 12. But I would not bet on that.

Also, there may be other octangular shapes.

Answer 1

9