Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.

__Asymptote code below__

**[asy] unitsize(1.5 cm);**

for(int i = 1; i <= 10; ++i) {

A[i] = dir(90 - 360/10*i);

draw(dir(90 - 360/10*i)--dir(90 - 360/10*(i + 1)));

}

draw(A[10]--(A[10] + A[2] - A[3])--(A[10] + A[2] - A[3] + A[4] - A[5])--(A[10] + A[2] - A[3] + A[4] - A[5] + A[2] - A[1])--(A[10] + A[2] - A[3] + A[4] - A[5] + A[2] - A[1] + A[4] - A[3]));

draw((A[10] + A[2] - A[3])--(A[10] + A[2] - A[3] + A[10] - A[1])--(A[10] + A[2] - A[3] + A[10] - A[1] + A[8] - A[9])--(A[10] + A[2] - A[3] + A[10] - A[1] + A[8] - A[9] + A[6] - A[7]));

dot(A[10]);

[/asy]

An equilateral triangle, a regular octagon, and a regular -gon, all with the same side length, also completely surround a point. Find .

Atroshus Aug 28, 2017

#1**+4 **

Best Answer

**Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.**

**An equilateral triangle, a regular octagon, and a regular -gon, all with the same side length, also completely surround a point. Find .**

**regular 24-gon**

heureka Aug 29, 2017