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In the most general sense, going back to Aristotle, the 'geosphere' is the region of space that is dominated by "geogenic" matter, that is, originating from and bound to the Earth. This is to be contrasted with the regions of space near the Earth that are dominated by matter from the solar atmosphere, known as the heliosphere. In the neighborhood of Earth, the heliosphere is dominated by the solar wind, a supersonic plasma flow radially away from the sun, throughout and far beyond the solar system of planets. The heliosphere also contains material ablated from the planets (including Earth) and their satellites, comets and asteroids, as well as material from the interstellar medium through which our solar system is moving as it orbits the galactic center.
The term 'geosphere' is often used less generally by geologists with reference to the densest parts of Earth, which consist mostly of rock and regolith. ^[1]. However, the term applies to the four nested geospheres identified since Meteorology (Aristotle) with the states of terrestrial matter: solid (earth), liquid (water), gas (air), and plasma (fire). The nested geospheres then include the asthenosphere, lithosphere, hydrosphere, atmosphere, and the ionosphere or plasmasphere. The dense geosphere is also subdivided into the crust, mantle, and core. The outer core is unusual in that it is considered to be a liquid, yet it is a part of Earth's interior.
Since space exploration began, it has been observed that the extent of the ionosphere or plasmasphere is highly variable, and often much larger than previously appreciated, at times extending to the boundaries of the Earth's magnetosphere or geomagnetosphere ^[2]. This highly variable outer boundary of geogenic matter has been referred to as the "geopause"^[3], to suggest the relative scarcity of geogenic matter beyond it, where the solar wind dominates.
In computer graphics geosphere can also mean a polygonal tessellation, or polyhedron, used to approximate a sphere. It also commonly named geodesic sphere.

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1. Skinner, B: "The Dynamic Earth.", page 21. John Wiley & Sons, Inc, 2000 ISBN 0-471-16118-7
2. Siscoe, G.: "Aristotle on the Magnetosphere, Eos Transactions of Am. Geophys. Un., v.72, pp. 69-70, 1991.
3. Moore, T.E. and D.C. Delcourt, The Geopause, Revs. Geophys., v32(2), p.175, 1995.