A radiate head or bust is depicted wearing a radiate crown. The radiate crown is an attribute of the Sun god (Sol Invictus, Helios) and is conferring that association upon the wearer. Tiberius was the first emperor to depict the radiate crown on coin portraiture, but ONLY for posthumous portraiture of the deified Augustus. Nero was the Roman first to depict it on a living person (himself). As a bust attribute on some roman coins it served as a "double value" denominational marker: dupondius = double as, antoninianus = double denarius.
Many coins of Rhodes depict the sun god Helios with a radiate crown. These images inspired the radiate crown on the Statue of Liberty.Rhodos, Carian Islands, c. 229 - 205 B.C.
Silver tetradrachm, SNG Keckman 548, SNG Cop -, Choice aEF, Rhodos mint, weight 13.403g, maximum diameter 26.3mm, die axis 0o, c. 229 - 205 B.C.; obverse radiate head of Helios facing slightly right; reverse RODI-ON, rose with bud right, thunderbolt left, magistrate's name EUKRATHS above.
Today we associate the crown with royalty. The ancient Greeks associated the radiate crown with divinity and in the Hellenistic period royalty was often associated with divinity. With the beautiful and rare type below Ptolemy IV honored his deceased father with the symbols of divinity. He wears the aegis of Zeus, the radiate crown of Helios, and carries the trident of Neptune.
Augustus, 16 January 27 B.C. - 19 August 14 A.D., Commemorative Struck by Caligula
Nero was the Roman first to depict it on a living person (himself). This was one act in a long list of egomaniacal behaviors that lead to rebellion against him and his suicide.
Nero, 13 October 54 - 9 June 68 A.D.
The radiate crown came to mean a double unit denomination. The dupondius was worth two as. Caracalla introduced a double denarius (antoninianus) and used the radiate crown to clearly identify its value.
Caracalla, 28 January 198 - 8 April 217 A.D.
Another example where the radiate crown is used to indicate a double value is the radiate crown on the double sestertius below.
Trajan Decius, July 249 - First Half of June 251 A.D.