@article{657.51014,
	title = {{Infinitesimally rigid polyhedra. II: Modified spherical frameworks.}},
	author = {Walter Whiteley},
	journal = {Trans. Am. Math. Soc.},
	number = {1},
	pages = {115-139},
	volume = {306},
	year = {1988},
	biburl = {http://www.bibsonomy.org/bibtex/296a1fae76d1ab96cd2788b8f30f15f79/dmartins},
	description = {robotica-bib},
	abstract = {{From the author's abstract: ``In the first paper [ibid. 285, 431-465
	(1984; Zbl 518.52010)] Alexandrov's Theorem was studied, and extended,
	to show that convex polyhedra form statically rigid frameworks in
	space, when built with plane-rigid faces. This second paper studies
	two modifications of these polyhedral frameworks: (i) block polyhedral
	frameworks, with some discs as open holes, other discs as space-rigid
	blocks, and the remaining faces plane-rigid; and (ii) extended polyhedral
	frameworks, with individually added bars (shafts) and selected edges
	removed. Inductive methods are developed to show the static rigidity
	of particular patterns of holes and blocks and of extensions, in
	general realizations of the polyhedron. The methods are based on
	proof techniques for Steinitz's Theorem, and a related coordinatization
	of the proper realizations of a 3-connected spherical polyhedron.''
	\par For example, the author proves the following type-(i) theorem:
	an abstract block and hole polyhedron, with a single k-gonal hole
	and a single k-gonal block, is generically isostatic if and only
	if the hole and block are k-connected (in a vertex sense). He gives
	complete definitions, rigorous proofs, and mentiones some related
	results and open problems.} },
	reviewer = {{J.Mueller}}, language = {English}, classmath = {{*51M20 Regular figures in space 52Bxx Polytopes and polyhedra 70C20
	Statics}},
	keywords = {4-connected Steinitz's Theorem} frameworks; generic graph; polyhedral rigidity; static {infinitesimal }
}