By　using　ab　initio　self-consistent-field　(SCF)　method,　the　geometry　optimization　of　the　C28,　C28C4,　C28H4　and　C28C　fullerenes　was　performed　in　Td　symmetry,　then　the　total-energy,　electronic　states　and　charge　distribution　were　calculated.　The　stability　of　clusters　was　determined　with　their　binding　energy.　It　is　found　that　the　C28,　C28C＇4　and　C28H4　clusters　are　stable,　but　C28C　is　not.　The　energy-gap　value　is　related　with　the　bonding　states　of　A-like　carbons　located　at　the　corners　of　Td-symmetry.　It　should　be　expected　that　the　hyperdiamond　with　C28　base　belongs　to　wide-gap　semiconductor　with　gap　of　about　3　eV.