Add a particle system to the object and set it up to make particles being emitted only from vertices.
Set up particle system
2 objects are needed for particle system to work, one as emitter, and another to be emitted.
Select emitter (sphere in your case), in Modifier Properties panel, add a Particle System for it.
A small ball (can be turned off) will appear near the emitter object to indicate it is a particle source, this ball is only visible in viewport, and will not be rendered
Go to Particle Properties panel, under Emission section:
- Leave it as Emitter
- Change Number corresponding to number of vertices in your emitter object. (How?)
You can see number of vertices of an object by entering edit mode, select all vertices by hitting a under vertex mode, and turn on Statistics under Viewport Overlays.
See: Vertex count number display
- Turn off Random Order in Source section.
- Change Emit From to Vertices
Other parameter you should care: in the Velocity section and Physics section, you'd like to turn off physical simulation and set velocity to 0, to prevent object being emitted at unwanted location (at render time).
For Emitted Object:
Again in Modifier Properties panel, add a Particle Instance for the object being emitted:
- modify the Object property, to point to emitter (use the eyedropper tool to select the emitter)
Here the cube is translated to some location for better illustration, if you reset the translation of cube, the particles will be perfectly aligned: