antiprism

An antiprism is a prismatoid whose bases are congruent and whose lateral faces are congruent triangles.

An antiprism can be used to construct an icosahedron: Let $A$ be an antiprism with regular pentagons as its bases and equilateral triangles as its lateral faces. To each base of $A$ , attach a pentagonal pyramid whose base is congruent to the bases of $A$ and whose lateral faces are equilateral triangles.

For any integer $n\\geq 3$ , the following are equivalent statements about an antiprism $A$ :

1.
$A$ has a base that is an $n$ -gon;
2.
$A$ has $2n+2$ faces;
3.
$A$ has $2n$ vertices;
4.
$A$ has $4n$ edges.

单词	Antiprism
释义	antiprism An antiprism is a prismatoid whose bases are congruent and whose lateral faces are congruent triangles. An antiprism can be used to construct an icosahedron: Let $A$ be an antiprism with regular pentagons as its bases and equilateral triangles as its lateral faces. To each base of $A$ , attach a pentagonal pyramid whose base is congruent to the bases of $A$ and whose lateral faces are equilateral triangles. For any integer $n\\geq 3$ , the following are equivalent statements about an antiprism $A$ : 1. $A$ has a base that is an $n$ -gon; 2. $A$ has $2n+2$ faces; 3. $A$ has $2n$ vertices; 4. $A$ has $4n$ edges.
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