Abstract. In this paper we develop the shape theory
for triads of spaces in a systematic way, using polyhedral
resolutions for triads of spaces, and give applications,
which include the Blakers-Massey homotopy excision theorem whose
proof is different from the approach taken by
1991 Mathematics Subject Classification. 54C56, 54C55, 55P55, 55Q07.
Key words and phrases. Shape, triad, homotopy excision, polyhedral triad, homotopy type.