Deltaedro

Deltaedro é um poliedro cujas faces são todas triângulos equiláteros. Há infinitos deltaedros, mas apenas oito são convexos:

Deltaedros convexos

Deltaedros convexos
Nome		Imagen	Faces		Arestas	Vértices		Simetria
P₁	Tetraedro regular		4	4 × te	6	4	4 × 3·3·3	T_d
J₁₂	Bipirâmide triangular		6	6 × te	9	5	2 × 3·3·3 3 × 3·3·3·3	D_3h
P₃	Octaedro regular		8	8 × te	12	6	6 × 3·3·3·3	O_h
J₁₃	Bipirâmide pentagonal		10	10 × te	15	7	5 × 3·3·3·3 2 × 3·3·3·3·3	D_5h
J₈₄	Disfenoide achatado		12	12 × te	18	8	4 × 3·3·3·3 4 × 3·3·3·3·3	D_2d
J₅₁	Prisma triangular triaumentado		14	14 × te	21	9	3 × 3·3·3·3 6 × 3·3·3·3·3	D_3h
J₁₇	Bipirâmide quadrada giralongada		16	16 × te	24	10	2 × 3·3·3·3 8 × 3·3·3·3·3	D_4d
P₅	Icosaedro regular		20	20 × te	30	12	12 × 3·3·3·3·3	I_h
te = Triângulos equiláteros

Freudenthal, H. and B. L. van der Waerden|van der Waerden, B. L. "Over een bewering van Euclides". ("On an Assertion of Euclid") Simon Stevin 25, 115—128, 1947. (They showed that there are just 8 convex deltahedra. )
H. Martyn Cundy Deltahedra. Math. Gás. 36, 263-266, Dec 1952. [1]
H. Martyn Cundy and A. Rollett Deltahedra. §3.11 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 142–144, 1989.
Charles W. Trigg An Infinite Class of Deltahedra, Mathematics Magazine, Vol. 51, No. 1 (Jan., 1978), pp. 55–57 [2]
Martin Gardner Fractal Music, Hypercards, and More: Mathematical Recreations, Scientific American Magazine. New York: W. H. Freeman, pp. 40, 53, and 58-60, 1992.
A. Pugh Polyhedra: A Visual Approach. Berkeley, CA: University of California Press, pp. 35–36, 1976.