Summary

Modified https://www.thingiverse.com/thing:2635317 to make it small enough to fit on a ring.

This ring is size 10. Or about 19.9mm

For my print I used electronron's method to add 2 pauses to the gcode so I could change the filament color.
https://www.thingiverse.com/groups/malyan-m200-mp-mini-select/forums/general/topic:11648

Print Settings

Printer Brand:

Monoprice

                                            <p class="detail-setting printer"><strong>Printer: </strong>                     <div><p>Select Mini</p></div></p>                                                                                <p class="detail-setting rafts"><strong>Rafts: </strong>                     <div><p>Doesn't Matter</p></div></p>                                                                                <p class="detail-setting supports"><strong>Supports: </strong>                     <div><p>Doesn't Matter</p></div></p>                                                                                <p class="detail-setting resolution"><strong>Resolution: </strong>                     <div><p>0.175</p></div></p>                                                                                <p class="detail-setting infill"><strong>Infill: </strong>                     <div><p>20</p></div></p>                                                        <br>                        <p class="detail-setting notes"><strong>Notes: </strong>                    </p><div><p>Printed this logo-side down so the Bionic Six emblem would be smooth as possible and it would be easier to change color.</p><p>However this leaves a substantial overhang where the ring reconnects.</p><p>You may also want to consider a raft if you have adhesion issues, because the logo only clings to the bed with very thin lines.</p></div>

Bionic 6 Ring