Task 635

The task

$ABCDEFGH$ shown below is a cube with volume 1. Find the volume of pyramid $ABCH$. [asy] import three; triple A,B,C,D,EE,F,G,H; A = (0,0,0); B = (1,0,0); C = (1,1,0); D= (0,1,0); EE = (0,0,1); F = B+EE; G = C + EE; H = D + EE; draw(B--C--D); draw(B--A--D,dashed); draw(EE--F--G--H--EE); draw(A--EE,dashed); draw(B--F); draw(C--G); draw(D--H); label("$A$",A,S); label("$B$",B,W); label("$C$",C,S); label("$D$",D,E); label("$E$",EE,N); label("$F$",F,W); label("$G$",G,SW); label("$H$",H,E); [/asy]