Just a random list of math terms for reference. I may revise this in the future.

Tessellations

4 transformations (dilate, transform, reflect, rotate) – specify object, specify angle of rotation and specify a center of rotation – dilate specify object, ratio, center –

translate (slide) – specify object, specify distance and specific direction

conjecture – guess not theorem

equilateral – not same as regular, diamond, rhombus

adjacent – next to

congruent – equal angles and lengths

prime, double prime

lattice

radius

perimeter

area – if area stays the same, perimeter increases when the shape is elongated (use all three together perimeter, area, and shape)

shape – if shape stays the same, perimeter and area change together

axiomatic structure

angle of rotation

postulate – assumed statement

theorem – provable statement

non euclidean geometry

ratio

midpoints

arbitrary circles

transitivity

Shapes

tetrahedron – 4 faces, 3 triangles, 1 vertex, can be classified as a pyramid, face type triangle, 4 faces, 6 edges, 4 vertices

cube – 6 squares, greatest number of squares to build a regular polygon, square face type, 6 faces, 12 edges, 8 vertices

dodecahedron – greatest number of regular pentagons at each vertex to build a polyhedron, 12 regular polygons, hexagon face type, 12 faces, 30 edges, 20 vertices

hexagon

Which of the Platonic solids can be classed as an antiprism? antiprism is same at top and bottom and has parallel planes, band of triangles, not tetrahedron be doesn’t pretend to be prisim but pyramid not parallel opposites, band of opposite triangles, octahedron and icosahedron are antiprisms

can do a Internet search for nets for the cube, octahedron, tetrahedron, dodecahedron, icosohedron, etc. Nets are fun to make and play with. Found some nice nets a few years ago at mathisfun.com