For her “Intersections” exhibition at the Phillips Collection, sculptor Arlene Shechet filled five galleries with her artworks, drawing inspiration from other works — and even the fireplaces. (Lee Stalsworth/Arlene Shechet/Sikkema Jenkins & Co.)

Arlene Shechet’s craggy sculptures might not seem an ideal fit for the Phillips Collection, known for its sunny Renoir and serene Rothkos. The New York artist’s creations are whimsical and wildly asymmetrical, a riot of shapes and textures. Squares, circles and tubelike projections stud the somewhat organic forms, and assure that the pieces appear different from every possible vantage.

Surveying the museum’s holdings, Shechet couldn’t locate a single item that spoke to her mixed-media but mostly ceramic pieces. She found dozens.

“Arlene Shechet: From Here On Now” is the latest in the Phillips’s “Intersections” series, in which a contemporary artist responds to the museum’s permanent collection. Shechet went bigger and further than her predecessors, and the results fill five galleries — four in the original mansion and one in the addition.

Shechet picked an eclectic selection of paintings, drawings and photographs from the collection. She included artworks the Phillips has never shown and one that was the impetus for another contemporary artist’s 2015 Phillips show. She even arranged aesthetic dialogues that address not the museum’s art, but its architecture.

Shechet’s sculptures are abstract, but many appear somewhat humanoid, or at least torso-like. The artist must agree with that observation, since she titled one of her creations “Go Figure” and placed it in the room with 15 portraits by the likes of Klee, Van Gogh, Mondrian and Diebenkorn. There’s also a Cezanne overlooking Shechet’s piece, which features a wavy steel ribbon that follows its contours.

Just around the corner from the salon-style array of portraits is a lone Walker Evans photo of a fetish-like African artifact. The piece, even in black-and-white and one dimension, looks more like Shechet’s work than anything else here. Although the object has a head and full limbs, “the form [is] related to my sculptures,” Shechet says in her notes on the exhibition.

Shechet decorated vases with patterns derived from floor plans of Buddhist temples. At center is Matisse’s “Interior With Egyptian Curtain.” (Lee Stalsworth/Arlene Shechet/ Sikkema Jenkins & Co.)

Many of the galleries in the Phillips mansion have fireplaces, which Shechet has accented with arrangements of bricks. One fireplace is framed by blue-and-white Delft tiles and earns a more complicated rejoinder: more than two dozen cast paper vases and their plaster molds, in the same color scheme. Blue-and-white porcelain is associated with Holland but began in China; Shechet salutes the style’s Asian origins by decorating the vases with patterns derived from floor plans of Buddhist temples.

The conversation continues with several still lifes painted in the late-19th and early-20th centuries, when Western artists first explored the possibilities of Asian art. Bowls and vases are among the pictorial elements in canvasses by Pierre Bonnard, Juan Gris, Man Ray and Henri Matisse. The Matisse just happens to be “Interior With Egyptian Curtain,” the departure point for Carol Brown Goldberg’s 2015 intersection with the Phillips legacy.

Inspired by one of the Phillips Collection fireplaces, Shechet cast a new base for her sculpture “The Possibility of Ghosts.” (Lee Stalsworth/Arlene Shechet/Sikkema Jenkins & Co.)

Another fireplace became the matrix that Shechet used to cast a new base for an existing sculpture, “The Possibility of Ghosts.” The artist’s pieces are usually multicolored, but this one is entirely gray. It sits in the most sparely appointed of the five galleries, accompanied by just one Phillips work, a large and sketchy Francis Bacon oil.

Much of the art that Shechet selected is representational. A large, soft-textured Joan Mitchell abstraction shares a room with the sculptor’s “Best Behavior,” whose hard ceramic tendrils seem to be melting and dripping. On the other side of the museum, the artist has placed four of her pieces in the company of abstractions by Morris Louis, Kenneth Noland and Josef Albers.

This gallery, the largest of the five, reveals contrasts and affinities. Shechet’s sinuous pieces echo the cool colors, fluid washes and grainy texture of the Louis painting, while their hard surfaces resemble the more geometric style of the two Albers. The Noland is somewhere in between, which may make it the most apt counterpoint of all.

Also in this room are six paintings by eccentric Texas recluse Forrest Bess, donated to the Phillips in 2014 but not yet shown there. Bess’s series of pictures of asteroids spurred Shechet to cast a new piece, “Seeing Asteroids,” for this exhibition.

Shechet’s enthusiasm for Louis, Mondrian and Van Gogh — to name just a few — is easier to understand than her taste for Bess. But most of the links between the contemporary artist and her precursors are intriguingly tangled. That inspiration is no simple matter is one of the lessons of this multifold show.

If you go
Intersections: Arlene Shechet: From Here On Now

Phillips Collection, 1600 21st St. NW. 202-387-2151.

Dates: Through May 7.

Prices: $12, students and seniors $10, age 18 and younger free.