# midsphere
## English
### Etymology

From mid- +‎ sphere.

### Pronunciation

* Audio (US):(file)

### Noun

midsphere (plural midspheres)
* A middle sphere or region.
** 1968, Space Aeronautics, volume 49, page 61:For rescue or personnel-transfer purposes, the midsphere could also, like DSRV, be equipped with a transfer bell.
** 1992, Carl Edmonds, Christopher Lowry, John Pennefather, Diving and Subaquatic Medicine, page 512:During a rescue operation, the mating system allows the transfer of rescuees from the disabled submarine to the midsphere of the DSRV via the transfer skirt which is rated to 20(K) feet.
* (geometry, solid geometry) The sphere which, if it exists, is tangent to every edge of a given polyhedron and with respect to which the polyhedron's vertices are the inversion poles of the planes of the faces of its dual polyhedron (and vice versa).
** 1999, Richard Padovan, Proportion: Science, Philosophy, Architecture, page 260:The edges are omitted as irrelevant to the present argument, but the midspheres are still included because Kepler rather casually substitutes the midsphere for the insphere of the octahedron, since it happens to give a value closer to the observed distance.
** 2003, Rona Gurkewitz, Bennett Arnstein, Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality, page 4:A face of a Catalan solid can be simply constructed by the Dorman-Luke construction [3, 4, 6, 16], which is based on a dualization process known as polar reciprocation [6], with respect to the midsphere.
** 2014, Walter Steurer, “Crystal Structures of Metallic Elements and Compounds”, in David E. Laughlin, Kazuhiro Hono, editors, Physical Metallurgy, 5th edition, volume 1, page 20:The Archimedean solids can all be inscribed in a sphere and in one of the Platonic solids. Their duals are the Catalan solids, with faces that are congruent but not regular (face-transitive); indtead of circumspheres like the Archimedean solids, they have inspheres. The midspheres, touching the edges, are common to both of them.
* (geometry) The sphere, between two given spheres, by which each of the latter may be inverted into the other.
** 1994, Tim Gallagher, Bruce Piper, Chapter 7: Convexity Preserving Surface Interpolation, Nickolas S. Sapidis, Designing Fair Curves and Surfaces, page 179,
    For any two circles (spheres) there always exists at least one midcircle (midsphere) which inverts the two given circles (spheres) into each other. in the older literature this is also known as the circle (sphere) of antisimilitude. […] The center of a midcircle (midsphere) is the center of similitude of two given circles (spheres). […] Clearly the midcircle (midsphere) of two equal circles (spheres) is the midline (midplane) between the two, which is partial justification for calling inversion in a circle or sphere reflection in a circle or sphere.
* (religion, Vedic mythology, uncountable) A supposed realm between earth and heaven.
** 2003, Ravi Prakash Arya, New discoveries about Vedic Sarasvatī, page 22:This celestial river (Nadī) transforms into [the] terrestrial one (sindhu) after falling from heaven (midsphere) in the form of rain-drops.
** 2005, Vishveshvaranand Indological Journal, volumes 43-44, page 48:The smoke emitted by a burnt solid being vikāra of gaseous water, experiences upward acceleration to join the midsphere water.
** 2009, Śaśi Tivārī, Alka B. Bakre, editors, Contemporary world order: a Vedic perspective, World Association for Vedic Studies, India Conference, page 173:The whole universe of these deities in divided in three spheres— earth, midsphere and sky.

#### Synonyms

* (sphere tangent to every edge of a polyhedron): intersphere, inversion sphere, reciprocating sphere
* (intermediate sphere by which each of two given spheres can be inverted into the other): sphere of antisimilitude

#### Related terms

* circumsphere
* insphere
* midcircle
* midradius

### See also

* canonical polyhedron
* inversion pole

### Further reading

* Inversive geometry on Wikipedia.Wikipedia
* Midsphere on Wolfram MathWorld