Observeu el tetràedre següent (que es presenta per mirar amb les ulleres 3D; desactiveu l'opció si no en disposeu)[br]Quina propietat diríeu que té té l'esfera que apareix?[br]Quina propietat ha de tenir el centre d'aquesta esfera?[br][br]Podreu girar la figura però no podreu moure els punts, que són molt especials els tetràedres amb aquesta propietat
Quin és el lloc geomètric dels punts que estan a la mateixa distància de dues rectes?[br]És un pla que es podria dir "pla bisector de dues rectes". Vegeu com es pot construir.[br][img 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[/img][br]Ho provem amb el GeoGebra?[br][br]Si fem els plans bisectors, per parelles, de les tres rectes que concorren en el vèrtex d'un tetraedre, quina propietat tindrà la recta intersecció? Comentem-ho, que resol geomètricament un problema interessant.[br][br]Perquè es pugui donar el cas d'una esfera com la que hem vist en l'applet anterior, el centre d'aquesta esfera ha d'estar a la mateixa distància de les sis arestes. La figura de l'applet deixa ben clar per què d'aquest punt els autors del treball en van dir [b]filcentre[/b]: va bé imaginar-se el tetràedre amb les arestes "de filferro".[br][br]Ben aviat es pot veure que no tots els tetràedres tenen filcentre. En la bibliografia, els tetràedres filcèntrics reben el nom de [i]tetràedres de Crelle[/i] o [i]esquelets[/i]. [br][br]El filcentre, si existeix, ha de ser la intersecció de tots els plans bisectors que acabem de comentar. [br]En sabríem triar tres que ja ens donessin el filcentre, cas d'existir?[br][br]En l'apartat següent suggerim alguns càlculs,