The artist found inspiration for many of these pieces following a 2,000-mile trip that he and his wife took through the western states of America.
He was fascinated by the natural landscape forms he found there but was equally captivated by manufactured objects, from product packaging to advertising graphics.
This clash of contrasts materialises in his work in the form of unusual juxtapositions, whether it's a cowhide sitting alongside neon plastic, or pendant lights embedded in a nest of raffia.
"It was just so rich, visually and culturally," Trayte told Dezeen. "I feel like it's going to have a legacy that lasts quite a while, in terms of how the work develops and what I make in the future too."
Trayte has made a wide variety of pieces for the exhibition, set to be titled MelonMelonTangerine. He describes the process as creating "a cast of characters".
"Quite often I will work on a group of things at the same time, and they come together like a weird bunch of misfits," he said.
By far the largest and most striking piece he has created is Sundown Swing, a swing bench attached to an abstract palm tree form, with a serpentine trunk.
"I wanted to make something outrageous," said Trayte, citing the late Austrian artist Franz West as an inspiration.
Trayte chose to give the tree black rubber leaves so that the piece could live outside in the future, but these elements also give the design a dark character.
"You can only use black rubber outside, because of the UV exposure," he said. "So it looks a bit more menacing than it was meant to be. It's scary, but it's still fun and ridiculous."
Some of the pieces are very blatant in their references to nature, such as the Atomic Double bench, the Black Dakota floor lamp and the Velvet Solar Star ceiling lights.
Others are more subtle in the way they bring together different colours, textures and forms, including the nest-like Jelly Baby seat and the furry orange chaise longue, Kula Sour.
"I hope these pieces transport the viewer to fantastical places," said Trayte.
"I wanted Kula Sour, for example, to look magical in its colour and its textures. Hopefully, the end-user will live with this, and it will transport them to wild landscapes and colourful Hawaiian Islands."
Trayte is very open about his intention to create function – and often multiple functions – in all of his works, even though he sees himself as a sculptor, not a furniture designer.
This tendency began with a cafe he created back in 2016, in collaboration with fashion designer Kit Neale. Trayte found it liberating to create works that could actually be used, not just sit in a gallery.
Since then he has incorporated furniture in many pieces, such as The Spectacle, a seating composition he created for London's Sculpture in the City series in 2016, and the first collection of works he presented at Friedman Benda, in 2018.
"I want to be as ambitious as possible, but also to make pieces that will find homes and get used," he said.