Rounding the edges leading to the peak will mean that the corners have to be rounded, too. It’s just sort of the geometry of the thing.
Well, doing this with no extensions is a little tricky but not really difficult. I leveraged a feature of the Follow Me tool that usually causes undesired results. this time it got me exactly what was needed.
First thing I did is make the pyramid into a component and unsure it is a solid. Entity Info on the right will let you know that. Then, on the bottom at one corner I drew an arc tangent to both edges. This is drawn outside of the pyramid component so it doesn’t attach itself to the pyramid’s geometry.
I then used the Line tool to draw some lines to create a horizontal face like so.
The lengths of those lines aren’t critical.
Next, with Line tool I drew a line from the corner of this new face parallel to the ridge line. Hover on the ridge for a moment after starting the line, then move the cursor up until you get the magenta parallel indication.
I used Follow Me to extrude the face along the line. Select the Line, get Follow Me, click on the face.
Note: In the vast majority of cases where you’ll use Follow Me you will need to make the profile perpendicular to the first segment of the path. Or you get a distorted profile. In this case, that distortion is exactly what we need.
Make that extrusion a component and check in Entity Info to see that it is considered solid. Next I made three more copies of that extrusion using Rotate/Copy. Select that extrusion component, get the Rotate tool. Press and release Ctrl to activate the copy function. I switched to the X-ray style so I could see the peak of the roof for the center of rotation.
Start the rotation of the copy, let go over the mouse and type 90, press Enter, type x3, press Enter. You should have a total of four copies of the component.
Next, I used the Subtract tool from the Solid Tools set found on the left side. the operation is: “Subtract this from that.” Get the tool, click on one of the corner extrusions and then on the pyramid. The extrusion should disappear leaving you with the round edge. Press Esc and then repeat, click an extrusion and then the pyramid. Repeat for each corner.
When you have finished that you can soften the edges between the flat faces and the rounded surfaces on the pyramid. Get the Select tool (Spacebar), triple left click on the pyramid component to open the component for editing and select all of the geometry. Right click on it and choose Soften/Smooth. that should take care of it.