TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Compounds: The aromatic polyene compound is divinylbenzene. The anion polymerization property vinyl compound monomer is aromatic vinyl compound monomer such as styrene. The anionic initiator is butyl lithium.    TECHNOLOGY FOCUS - POLYMERS - Preferred Composition: The mass ratio of ethylene-aromatic vinyl compound-aromatic polyene copolymer is 40-95 mass% with respect to the cross-copolymer. A resin composition consists of cross-copolymer, aromatic vinyl compound polymer and olefin type polymer, or cross-copolymer and block copolymer. Preferably, the resin composition contains cross-copolymer (70-99 mass%) and petroleum resin or hydrogenated petroleum resin (1-30 mass%). Preferred Properties: The 1 mm thickness sheet formed using cross-copolymer has haze of 30% or less and total light transmittance of 75% or more. The cross-copolymer has initial-stage tensile elasticity modulus of 10-150 MPa, elastic recoverability of 50% or more, thickness reduction rate of 15% or less in heating deformation test, abrasion loss of 100 mg or less in Taber's abrasion resistance test, and reduced film anisotropy (initial-stage tensile-elasticity modulus ratio of machine direction and transverse direction of 1-2). The weight average molecular weight of ethylene-aromatic vinyl compound-aromatic polyene copolymer is 30000-150000. EXAMPLE - Divinyl benzene, cyclohexane (4400 ml), and styrene (400 ml) were polymerized at 60 degrees C in presence of nitrogen. Then, triisobutyl aluminum (8.4 mmol) and methyl alumoxane (12.6 mmol) were added and heated at 100 degrees C. Ethylene was introduced immediately and maintained under pressure of 0.5 MPa. Toluene solution (30 ml) containing triisobutyl aluminum (0.98 mmol) and rac-dimethyl methylene bis(4,5-benzo-1-indenyl)zirconium dichloride (40 mu mol) was added to the reaction liquid and polymerized at 100 degrees C and 0.5 MPa pressure. Secondary butyl lithium (26 mmol) was added and anion polymerization was carried out at 60-80 degrees C. The obtained polymerization liquid was gradually added to methanol, stirred and polymer was recovered. The obtained polymer was dried, to obtain cross-polymer (675 g). The obtained cross-copolymer had total styrene content of 23.9 mol%, and melting temperature of 72 degrees C. A sheet formed using the composition containing cross-copolymer had haze value of 12%, total light transmittance of 82%, breaking point stress of 17 MPa, elongation at break of 760%, initial-state tensile elasticity modulus of 19 MPa, and stress in 100% elongation of 5 MPa.