Orthographic (engineering) drawing with same top and front view?

I came across this while reading on third angle orthographic projections.

The object has the exact same front and top view - both views are trapeziums of exact shape and size (As shown in the image). Also there is a hidden circle center line right thorough the middle of both of them.

I am unable to complete the projection as I cannot visualize this object - so I can't work out the right and left views.

The single image represents both the front and top views - I can't work out the left and right views.

I'm not convinced that the line is for a hidden feature. I would imagine the line indicates that entire part is revolved about the indicated axis. Naturally if the part has cylindrical symmetry, the top and front views can be made identical by proper orientation of the body relative to the drawing.

Assuming my understanding of the drawing is correct, I imagine the part to be a right conical frustum, which would look something like this MathWorld entry, or as seen below. Simply rotate the 2D image 90 degrees counter-clockwise to achieve a proper orientation.

However, if there is a hidden feature, then the part could look like a right square pyramidal frustum with a hidden hole, as shown here.

• Of course, there are any number of ways to deform these shapes while keeping the top and front projections unchanged. Such is the difficulty of representing N-dimensional objects with lower-dimensional projections.
– Air
Jul 31 '15 at 3:48

A simple way to approach a problem like this is to imagine that you are starting out with a block of material larger than your desired object. This is the "blank" out of which you'll fabricate, in your mind's eye, the 3D object with the maximum volume that could possibly satisfy your 2D projections.

Now imagine you have somehow projected the front view onto the front face of your blank—or, whichever view onto the corresponding face. After projecting the front view image onto the front face of the blank, you must remove all the material that falls outside of the image. When you remove material from the face, you remove everything behind it, as though you're shooting straight through from front to back, parallel to the path of the projector beam. (Alternatively, if you like shop tools, think of tracing the projected shape and then setting your blank face-up on a band saw or drill press to remove material.)

You should be able to see that projecting a perfect circle onto the front face of your blank would lead you to cut out a cylinder. In this first step, your result is simply an extrusion of the projection perpendicular to its surface, whatever its shape.

The second step (and beyond, if applicable) is where it gets interesting. In your mind, reorient yourself so that you're looking from the perspective of your next view, and project the corresponding image onto that face. Repeat the process of drilling out/cutting away anything outside of the projected image, being careful to go straight through, perpendicular to line of sight in your new orientation.

If you go through this process with identical trapezoids as the top and front view, you get the right square pyramidal frustrum (or, in slightly less technical language, truncated square pyramid) from starrise's answer, without the hidden hole. This is the maximum possible volume that satisfies the constraints of your top and front view.

It's not, however, the only possible volume. You can poke all sorts of skew holes through the object; you can round the corners, and if you round them enough, you'll get a truncated cone. One actual component of less-than-maximum volume that your trapezoidal views bring to mind is a pipe flange, something like this but with more prominent ribs:

This approach is more than just a mental exercise. If you wanted, using an actual block of wood, an overhead projector and some transparency sheets, you could actually manufacture that max-volume square pyramid using your trapezoid shape. Or, you could replicate the cover illustration of Gödel, Escher, Bach:

In the above image, the top/bottom and side views are projected through the finished component, revealing the orthogonal shapes that you would have to cut from a blank to produce a (maximum volume) reproduction of that component.

Starrise is right. The 'dot-dash' line is standard notation for a centre line and the 'trapezium' is part of the standard notation to indicate first angle or third angle projection. The end view is two concentric circles - positioned to the right of the 'trapezium' indicates first angle projection, positioned to the left indicates third angle projection. See the Wikipedia entry 'multiview orthographic projection'.