Playground

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31paper square

; triangle
fold (map .a onto .c) as --bd

; preliminary base
reverse (map .b onto .c) as --h
reverse (map .d onto .c) as --v

; apex O, the paper centre
.o = --h * --v

; centre line of the base
--mid = (through .c .o)

; front-right corner: paper (1/2,0) table (1,1/2)
.sr = --ab * --h
reverse (map .sr onto --mid through .c)

; front-left corner: paper (0,1/2) table (1/2,1)
.sl = --da * --v
reverse (map .sl onto --mid through .c)

; back-right corner: paper (1, 1/2)
.br = --bc * --h
reverse (map .br onto --mid through .c)

; back-left corner: paper (1/2, 1)
.bl = --cd * --v
reverse (map .bl onto --mid through .c)