The augmented icosahedron is is made by attaching one (tetrahedron) pyramid to each face of the [simple icosahedron|icosahedron#simple], retaining the same symmetries. images/constructed/dscn1651.jpg images/constructed/dscn1652.jpg images/constructed/dscn1653.jpg In total you'll need: COMPONENTS AMOUNT NOTES vertices of 3 20 pyramid pinnacles, one per face of icosahedron vertices of 10 12 icosahedron vertices edges 90 30 (icosahedron) + 20 x 3 (pyramid extras) images/constructed/dscn1658.jpg ((An insider look at the different types of vertices: bright pink (3-vertices), dark purple (10-vertices))) The augmented icosahedron is part of the [icosahedron-in-dodecahedron].