Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.

The Euler's formula relates the number of vertices, faces and the edges of a polyhedron. The given polyhedron has 6 vertices, 10 edges and 6 faces

The Euler's proof is:

First, we count the number of faces of the polyhedron.

This is the flat parts of the shape.

The attached shape has 6 flat surfaces.

So:

Next, we count the number of edges.

This is where two faces meet.

The attached shape has 10 edges;

So:

Lastly, we count the number of vertices.

This is where two edges meet.

The attached shape has 6 vertices.

So:

Using Euler's formula, we have:

Substitute values for V, E and F

Hence, the polyhedron has 6 vertices, 10 edges and 6 faces

Read more  vertices, edges, and faces at:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.