Tesselating hex height fields

I’m thinking of using the OpenGL API to write a 3D Terrain viewer for hex-based games, using GL_TRIANGLE_FANs for the hex surfaces and GL_QUAD_STRIPs for any exposed hex sides. However, I’m a little concerned about the large number of polygons that would be generated. Assuming a medium-size game terrain of 40x40 hexes, this would mean creating 1600 GL_TRIANGLE_FANs with 6 triangles per fan/hex. Each exposed rectangular hex side would require 2 triangles. Depending on the number of different terrain elevation levels, the number of polygons just for the exposed hex sides would also be rather large. The question then becomes: Is tesselating hex height fields even feasible?