Excited to see an unexpected set of plans in the mail, I ignored the accompanying cover letter and took a quick look. The plans showed a nearly round addition to an elegant 1888 Victorian that would enclose a new window-filled dining area. They also called for a gut and remodel of the kitchen and adjoining bath downstairs, and a new master bathroom upstairs.

After reading the accompanying project documents more carefully, I realized that there were a lot of details that would make bidding difficult — but my main concern was the dining room. Could we build it without losing our shirts in the process? Eager to get this interesting project, my partner and lead carpenter Danny DoCouto pointed out that the room was essentially a regular 16-sided polygon. While the angles would slow us down a little, the actual construction — he assured me — wouldn’t be all that different from the more typical rectangular additions we usually build.

### Foundation Layout

Normally we would build the foundation on a project like this. But the adjoining part of the old house had so many problems — including undersized girders and rotten joists and posts — that needed to be addressed during the renovation, we decided to sub out the new foundation. That way we could repair the existing structure while the masonry work was being done and be on site to oversee the layout of the foundation.

The total width of the addition measured 15 feet from sill to sill, with the polygon overlapping the existing house at the sill plate by 6 inches. This put the center point of the addition 7 feet away from the outside edge of the existing sill, and the outer edge of the new polygon foundation 14 feet 6 inches away.

• Dividing the 360 degrees of a circle by the number of sides in a regular polygon gives you the apex angle (here, 22.5 degrees) of the isosceles triangles that can be drawn around the center. Bisecting this angle gives a right triangle that can be used to solve for the lengths of the sides (x) with either a Construction Master calculator or trig function (for example, tan 11.25 = opposite/adjacent). The answer? x = 2 feet 11 13/16 inches.

A 16-sided polygon can be divided into 16 equal isosceles triangles, each with a central angle of 22.5 degrees (360 divided by 16). Using this angle and the 7-foot 6-inch distance from the center of the addition to the midpoint of each side, we calculated the length of the sides.

Before digging the hole, we opened up the side of the house to benchmark the height of the existing foundation and floor framing and to locate the center of the new 10-foot 6-inch opening that would connect the house to the addition. With those dimensions for reference, we outlined the rough perimeter of the foundation with spray paint, then used a rented mini-excavator to dig a hole that would put the bottom of the 12-inch-thick footing more than 36 inches below grade — below frost depth for our part of New Jersey.

Trench footing. I suggested that, instead of building the angled footing form shown on the plans, the masons pour a much simpler 2-foot-wide circular trench footing — a change I ran by the building inspector. From the center of the opening, we strung a perpendicular line off the house, then measured 7 feet out from the sill and drove a form pin into the ground directly underneath this point. From that center pin, we swung 6-foot and 8-foot arcs representing the inside and outside of the footing trench.

The addition’s block foundation was built on a circular trench footing, laid out from the center point of the 16-sided polygon.

The 12-inch-deep by 2-foot-wide footing was dug by hand in the bottom of the excavation and reinforced with rebar.

Because the 16-sided room isn’t freestanding, the footing layout had to deviate from its circular shape as it approached the house, creating more of a horseshoe shape. The masonry crew hand-dug the 12-inch-deep footing trench, laid up the rebar on chairs, and poured the footing.

To lay out the block wall, we made a plywood template designed to pivot on the center pin and used it to mark the sides of the wall on top of the footings. Starting at the outermost wall segment, we moved the template left and then right, marking 11 segments on the footing. We turned the next wall section on each side to intersect the house at 90 degrees, as indicated in the illustration.

To lay out the foundation, the author cut a plywood template based on the dimensions of one of the isosceles triangles that make up the 16-sided polygon. The template registers against the form pin at the center of the addition; the end of the template represents each 2-foot 11 13/16-inch side of the polygon.

Block foundation. Because of all the angles, it made more sense to stack the block than to use a running course. To strengthen the wall, the mason used Durawall galvanized mesh to overlap each joint and poured the cores, adding vertical rebar on each side of the angles. To help the mason check his work while laying up blocks, Danny mocked up a sill out of a pair of 2x4s cut at 11.25 degrees and joined together.

The stacked blockwork was reinforced with galvanized wire mesh on each course. A mock 2x4 sill cut to the exact angle and dimensions of two wall sections helped the masons get the corners right as they laid up block.

While virtually every other block needed to be cut to fit, the foundation was only five courses high, so it didn’t take long to build. Once the masons finished parging and dampproofing, they laid a vapor barrier and reinforcing mesh on the inside and poured a 4-inch-thick rat slab. Before backfilling, we also installed a 4-inch-diameter perforated footing drain protected by a fabric sock.