This shape being created in a 2D illustration program is not entirely possible in 3D without some distortion. That being said a close approximation may be achieved.

It's a bit of an involved process so I won't go into full details here, but I'll try to get the main steps. Here's the rough procedure of what I could come up with.
- Create a bezier curve circle
- Rotate it so it faces the front view
- Rotate it 60º in the Z axis
- Erase the back half
- Duplicate it in edit mode so it is symmetrical along the Y axis
- Repeat the process by duplicating the two half circles and rotating them 90º in Y axis so the produce the two frontal horizontal loops.
- Now the tricky part is making sure you selecting the correct overlapping end vertex and connect them to the proper corresponding loose end by pressing the F key
- Repeat the process 3 times. For the last closing loop just Toggle Cyclic option for the selected spline from the Properties Window
- This will make half the necessary loops. Luckily the remaining ones are just a copy of the current ones rotated 45º along the Y axis, then scaled negatively -1 unit along the 7 axis to complete all the loops.

Afterwards you may add a flat segment bezier curve as Bevel Object to make the ribbon shape.
You may also optionally add a Shrinkwrap modifier to a sphere object to approximate the shape into a more accurate sphere.
If you want thickness a Solidify modifier after the Shrinkwrap will do the trick.

Fto connect them no duplication required. The tricky part is the curves are all overlapping so it is hard to select the correct vertex. It might be easier if you just hide the splines not needed for the current step withHkey. Just select one point of the spline, pressCtrl+Lto select all linked thenHto hide. – Duarte Farrajota Ramos Jan 27 '18 at 18:42I am able to get to step 8 and I have all the vertices connected. From what I see, you are duplicating after step 8 and rotating it 90 along the z axis...? The last frame in the GIF you sent showing how to connect the vertices is what I am unable to create.
– frowest Feb 01 '18 at 00:31