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The polygon command in AutoCAD: I and C give different sizes

The polygon command in AutoCAD takes one radius, but typing I or C with the same number gives two different sizes. We measured both on AutoCAD 2027.

  • TS. Đỗ Quốc Hoàng
  • 8 min read
Two hexagons built from the same radius of 1000 on AutoCAD 2027: type I and the corners sit on the circle, type C and the edges touch it Photo: Screenshot taken on AutoCAD 2027 at the Institute

You are drawing a hexagon nut, or a column with an eight-sided opening. You run the command, type the radius exactly as the original drawing gives it, and the shape still comes out wrong. The polygon command in AutoCAD goes wrong at one point only: it asks a question that a great many people answer out of habit.

This article measures both answers on AutoCAD 2027 at the Institute and checks them by hand. For a full grounding in drafting see our AutoCAD for Construction course.

Where to start it

Read straight out of the acad.cuix interface file of the 2027 release on the machine.

RouteDetail
Full commandPOLYGON
AliasPOL
RibbonHome → Draw → Rectangle Drop-down → Polygon
Classic menuDraw → Polygon
ToolbarDraw → Polygon

On the ribbon it hides inside the Rectangle drop-down, so you have to click the little arrow to find it. That is why people who have used AutoCAD for years still draw polygons by rotating one line at a time.

Autodesk sums it up in four words on the POLYGON page for the 2027 release: "Creates an equilateral closed polyline". Two parts matter: equilateral, so every side is the same, and closed polyline, so the result is one object.

We checked it on the machine: the object created is an LWPOLYLINE, a single entity rather than six separate lines. One click selects the whole shape, and its area can be read straight off.

Step by step on the command line

The middle column is copied verbatim from AutoCAD 2027.

StepWhat the program asksWhat you do
1Enter number of sides <5>:Type the number of sides, say 6
2Specify center of polygon or [Edge]:Click the centre, or type E to work from a side
3Enter an option [Inscribed in circle/Circumscribed about circle] <I>:Type I or C
4Specify radius of circle:Type the radius

Step 3 decides everything, and most of this article is about it. Everything else in the polygon command in AutoCAD is routine, and nobody gets it wrong.

On step 1, the program only accepts a range. We tried 2 and 1025, and both times it answered, verbatim:

Requires an integer between 3 and 1024.

Type 3 or 1024 and it accepts them without complaint. A 1024-sided polygon looks like a circle, but it is still a polyline, so it weighs far more in the drawing than a real circle would. On a drawing with many of them the difference in file size is easy to notice.

The inscribed option and the circumscribed option

This is the heart of it. We drew two regular hexagons, both with a radius of 1000, changing nothing but the letter typed at step 3, then measured the bounding box and area of each.

Two options, one radius Photo: The measurements for Inscribed and Circumscribed on AutoCAD 2027, with the hand arithmetic to check them
AnswerWidth × heightArea
I2000.00 × 1732.052,598,076.2
C2309.40 × 2000.003,464,101.6

The same figure of 1000, and the C shape comes out noticeably larger. Its area is exactly four thirds of the other.

The reason lies in what that radius measures to. Autodesk spells it out for each option. For Inscribed in circle: "Specifies the radius of a circle on which all vertices of the polygon lie" — the circle through every corner. For Circumscribed about circle: "Specifies the distance from the center of the polygon to the midpoints of the edges" — out to the middle of a side.

The picture at the top shows precisely that. One red circle of radius 1000 in each case: on the left six corners touch it, on the right six edges touch it.

Check it against the geometry. A regular hexagon inscribed in a circle of radius R has its opposite corners 2R apart, which is 2000 — matching. Its height across opposite flats is 2R times the cosine of 30 degrees, which is 1732.05 — also matching.

Why the two words are so easily swapped

The confusion is purely one of grammar, and it is worth naming.

In AutoCAD's English the subject is the polygon: polygon inscribed in circle means the polygon sits inside the circle. In most school geometry, people name the circle instead: the circumscribed circle of a polygon, the inscribed circle of a polygon.

The two phrasings run in opposite directions, and that single mismatch accounts for most of the shapes that come out the wrong size. This table is worth keeping:

You typeAutoCAD's phrasingThe circle, named the other way
Ipolygon inscribed in circlethe circumscribed circle of the polygon
Cpolygon circumscribed about circlethe inscribed circle of the polygon

The safest habit is to drop both words entirely and ask one question instead: does my radius reach a corner or the middle of a side? A corner means I; the middle of a side means C.

In mechanical and structural practice, the size quoted for a hexagon nut or bolt head is the distance across the flats, the spanner size. That is twice the distance from centre to mid-side, so it calls for C and half of the quoted figure.

The edge option: give the side length directly

When the drawing gives a side length rather than a radius, there is no need to work backwards. At step 2, type E and press Enter, and the program asks two questions:

Specify first endpoint of edge:
Specify second endpoint of edge:

Click the two ends of one side and it builds the rest. Autodesk calls it "Defines a polygon by specifying the endpoints of the first edge".

We measured it with a side of 1000 and six sides. The result: 2000.00 × 1732.05, area 2,598,076.2 — identical to the I hexagon of radius 1000 above.

That is not a coincidence. For a regular hexagon alone, the side length equals the radius of the circle through the corners. For a pentagon or an octagon the two differ, so do not carry the habit across.

One more thing about Edge: the direction you click decides which side the shape falls on. Click left to right and the polygon builds upwards; click the other way and it flips below.

Drawing a hexagon and then editing it

Because the result is a closed polyline, every polyline command works on it.

To round the corners, type F for FILLET, choose Polyline and pick the shape, and all six corners round in one go. How to use it is covered in our article on the fillet command.

To change the line width of the whole shape, type PE for PEDIT and choose Width. That is covered in our article on polylines in AutoCAD.

For the area, select the shape and press Ctrl+1 to read the Area field, with no measuring command at all.

One habit worth forming on repetitive work: draw the polygon once, turn it into a block, and insert it wherever it is needed. A hexagon nut that appears forty times on a drawing then carries one definition rather than forty, and a change to the size reaches every copy at once.

For an irregular polygon, this command is no help. It only builds regular shapes, exactly as the word equilateral in the documentation says. Irregular outlines are drawn with PL, clicking each corner.

Three things people say that are not true

What people sayWhat the 2027 release actually does
I and C give the same shape, just named differentlyAt a radius of 1000, I gives 2000 × 1732 and C gives 2309 × 2000
The radius you type is the inscribed circle of the polygonOnly with C. With I it is the circle through the corners
Any number of sides will doOnly 3 to 1024. Outside that it reports Requires an integer between 3 and 1024.

The polygon command in AutoCAD is four answers long, and three of them nobody gets wrong. The fourth is the one worth a second's thought, because it is the only one where a perfectly reasonable answer still produces the wrong shape.

Frequently asked questions

What is the alias?

POL. The full name is POLYGON, and on the ribbon it hides in the Rectangle drop-down.

Should I type I or C?

Ask what your radius measures to. A corner means I; the middle of a side means C.

How do I draw a hexagon to a spanner size?

The spanner size is the distance across the flats. Type C and give half of it.

What is the largest polygon I can draw?

1024 sides. Below 3 or above 1024 the program refuses with a single line.

What if I know the side length but not the radius?

Use the Edge option: type E when asked for the centre, then click the two ends of one side.

Can it draw an irregular polygon?

No. It only builds regular shapes. Irregular outlines are drawn with PL, corner by corner.

About the author

TS. Đỗ Quốc Hoàng — Vice Director of the Institute of Information Technology in Civil Engineering, Hanoi University of Civil Engineering, and a specialist in software development for construction