The steps I used to create the following design.
Click on any image for a larger view.
Draw a teardrop shape.
Change the rotational centre as shown below.
I changed colours as it was hard to see on the black.
Align the modified teardrop shape as shown below.
Duplicate and rotate 36 degrees.
Duplicate the teardrop you just rotated and rotate it 36 degrees.
Repeat until design is complete.
To finalise, select all and apply Path>Union.
Tidy up any stray nodes.
Settings are shown below for rotating the teardrop.
The basic shape can now be used to make borders or mats.
Example shown below.