This is a list from OMIM of syndromes associated with triphalangeal thumbs:
*190605 triphalangeal thumb-polysyndactyly syndrome
*174500 polydactyly, preaxial ii; ppd2
*188770 tibia, hypoplasia of, with polydactyly
*190600 triphalangeal thumb, nonopposable
205600 anemia and triphalangeal thumbs
*190680 triphalangeal thumbs with brachyectrodactyly
190650 triphalangeal thumbs and dislocation of patella
179250 radial hypoplasia, triphalangeal thumbs, hypospadias, and maxillary diastema
190500 triphalangeal thumb with double phalanges
#107480 townes-brocks syndrome; tbs
#142900 holt-oram syndrome; hos
*174600 polydactyly, preaxial iii
*220500 deafness, congenital, and onychodystrophy, recessive form
#174400 polydactyly, preaxial i
141400 hemifacial microsomia with radial defects
154400 acrofacial dysostosis 1, nager type; afd1
*149730 lacrimoauriculodentodigital syndrome; ladd
300233 radioulnar synostosis, radial ray abnormalities, and severe malformations in the male
256690 neurofaciodigitorenal syndrome
*147800 aase-smith syndrome
138790 goiter, multinodular, cystic renal disease and digital anomalies
#205900 diamond-blackfan anemia; dba
192350 vater association
*600725 sonic hedgehog, drosophila, homolog of; shh