2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60477A Clifford algebra Cl(V,η\in V^*\otimes V^*) jointly with a Clifford cogebra Cl(V,ξ\in V\otimes V) is said to be a Clifford biconvolution Cl(η,ξ). We show that a Clifford biconvolution for dim_R Cl=4 does possess an antipode iff det(id-ξ\circη)\neq 0. An antipodal Clifford biconvolution is said to be a Clifford Hopf gebra. We study the Clifford Hopf gebra and examples of antipode less Clifford bigebras including the Grassmann case.14 pages, 8 eps-figure, submitted to `Miscellanea Algebraica' Kielce, PolandQuantum AlgebraHigh Energy Physics - Theory15A66; 16W30text