Stylophora (cornutes and mitrates) are controversial Paleozoic fossils, var
iously interpreted as 'bizarre' echinoderms or as 'calcichordates' (primiti
ve chordates). The calcichordate theory is based on the identification of l
eft/right asymmetries supposed to be homologous in stylophorans and modern
chordates. This theory imposes the homology of the plano-concave surface of
the cornute test with the convex surface of the mitrate test. A detailed a
nalysis of numerous internal and external structures exhibited by the appen
dage and the test demonstrates the homology of the plano-concave surface of
the test in all stylophorans. The basic assumption of the calcichordate th
eory is thus not valid, Comparison of left/right asymmetries in these organ
isms with those of modem chordates is not grounded. Stylophora do not; repr
esent 'calcichordates' but actual echinoderms.