A squaricle is a creased D-form constructed by joining the boundaries of a disk and a square with equal perimeters (Sharp 2005, p. 123). It is a spatial surface and should not be confused with the planar squircle.
For a disk of radius 
,
the square has side length 
, so the total surface
area is
 |
(1)
|
The symmetric construction consists of four generalized cone patches from the disk, four generalized cylinder patches from the square, and a central planar square (Sharp 2005, p. 123). Its height above the planar base is
 |
(2)
|
Each of its four radial creases has length 
, and the joining seam has length
. The Gaussian
curvature vanishes on the smooth patch interiors. An elementary piecewise parametrization
gives the enclosed volume
 |  |  |
(3)
|
 |  |  |
(4)
|
