The recently accepted new mineral flamite IMA No. 2013-122, (Ca,Na,K)(2)(Si,P)O-4, found in the pyrometamorphic rocks of the Hatrurim Formation, Israel, was reported to crystallize in the hexagonal space group P6(3) with unit-cell parameters a = 43.3726(18), c = 6.8270(4) angstrom. A careful re-examination of single crystals from the type locality and holotype material, however, shows that flamite is better described by the formula Ca8-x(Na,K)(x)(SiO4)(4-x)(PO4)(x) and that it crystallizes in the space group Pnm2(1), a = 9.3845(6), b = 21.7310(14), c = 6.8346(4) angstrom, V = 1393.81(15) angstrom(3), Z = 4 and is isostructural with the known synthetic P-doped clinker phase Ca-15 square(SiO4)(6)(PO4)(2). The structure is a derivative of the hexagonal high-temperature variety of dicalcium-silicate, alpha-C2S, and is characterized by a cyclic triplet of individuals rotated 120 degrees around c, interpreted as symplectite-like transformation "twinning" derived from alpha-C2S. The composition of intergrown flamite lamellae is chemically variable concerning the degree of Na, K and P substitution. We present the structure of flamite and discuss its close relationship to nagelschmidtite, Ca-7(SiO4)(2)(PO4)(2), and the high-temperature polymorphs of C2S.